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[Core] Move Rect2 and Transform2D to their own files
Math2D includes Transform2D, which includes Rect2, which includes Vector2.
This commit is contained in:
Aaron Franke
parent
9170d932e3
commit
2eb8a9749e
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@ -30,64 +30,6 @@
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#include "math_2d.h"
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bool Rect2::intersects_segment(const Point2 &p_from, const Point2 &p_to, Point2 *r_pos, Point2 *r_normal) const {
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real_t min = 0, max = 1;
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int axis = 0;
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real_t sign = 0;
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for (int i = 0; i < 2; i++) {
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real_t seg_from = p_from[i];
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real_t seg_to = p_to[i];
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real_t box_begin = position[i];
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real_t box_end = box_begin + size[i];
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real_t cmin, cmax;
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real_t csign;
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if (seg_from < seg_to) {
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if (seg_from > box_end || seg_to < box_begin)
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return false;
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real_t length = seg_to - seg_from;
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cmin = (seg_from < box_begin) ? ((box_begin - seg_from) / length) : 0;
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cmax = (seg_to > box_end) ? ((box_end - seg_from) / length) : 1;
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csign = -1.0;
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} else {
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if (seg_to > box_end || seg_from < box_begin)
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return false;
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real_t length = seg_to - seg_from;
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cmin = (seg_from > box_end) ? (box_end - seg_from) / length : 0;
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cmax = (seg_to < box_begin) ? (box_begin - seg_from) / length : 1;
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csign = 1.0;
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}
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if (cmin > min) {
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min = cmin;
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axis = i;
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sign = csign;
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}
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if (cmax < max)
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max = cmax;
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if (max < min)
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return false;
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}
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Vector2 rel = p_to - p_from;
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if (r_normal) {
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Vector2 normal;
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normal[axis] = sign;
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*r_normal = normal;
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}
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if (r_pos)
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*r_pos = p_from + rel * min;
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return true;
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}
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/* Point2i */
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Point2i Point2i::operator+(const Point2i &p_v) const {
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@ -153,244 +95,3 @@ bool Point2i::operator!=(const Point2i &p_vec2) const {
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return x != p_vec2.x || y != p_vec2.y;
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}
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void Transform2D::invert() {
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// FIXME: this function assumes the basis is a rotation matrix, with no scaling.
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// Transform2D::affine_inverse can handle matrices with scaling, so GDScript should eventually use that.
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SWAP(elements[0][1], elements[1][0]);
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elements[2] = basis_xform(-elements[2]);
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}
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Transform2D Transform2D::inverse() const {
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Transform2D inv = *this;
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inv.invert();
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return inv;
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}
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void Transform2D::affine_invert() {
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real_t det = basis_determinant();
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#ifdef MATH_CHECKS
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ERR_FAIL_COND(det == 0);
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#endif
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real_t idet = 1.0 / det;
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SWAP(elements[0][0], elements[1][1]);
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elements[0] *= Vector2(idet, -idet);
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elements[1] *= Vector2(-idet, idet);
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elements[2] = basis_xform(-elements[2]);
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}
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Transform2D Transform2D::affine_inverse() const {
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Transform2D inv = *this;
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inv.affine_invert();
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return inv;
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}
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void Transform2D::rotate(real_t p_phi) {
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*this = Transform2D(p_phi, Vector2()) * (*this);
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}
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real_t Transform2D::get_rotation() const {
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real_t det = basis_determinant();
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Transform2D m = orthonormalized();
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if (det < 0) {
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m.scale_basis(Size2(1, -1)); // convention to separate rotation and reflection for 2D is to absorb a flip along y into scaling.
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}
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return Math::atan2(m[0].y, m[0].x);
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}
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void Transform2D::set_rotation(real_t p_rot) {
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real_t cr = Math::cos(p_rot);
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real_t sr = Math::sin(p_rot);
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elements[0][0] = cr;
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elements[0][1] = sr;
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elements[1][0] = -sr;
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elements[1][1] = cr;
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}
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Transform2D::Transform2D(real_t p_rot, const Vector2 &p_pos) {
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real_t cr = Math::cos(p_rot);
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real_t sr = Math::sin(p_rot);
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elements[0][0] = cr;
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elements[0][1] = sr;
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elements[1][0] = -sr;
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elements[1][1] = cr;
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elements[2] = p_pos;
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}
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Size2 Transform2D::get_scale() const {
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real_t det_sign = basis_determinant() > 0 ? 1 : -1;
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return Size2(elements[0].length(), det_sign * elements[1].length());
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}
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void Transform2D::scale(const Size2 &p_scale) {
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scale_basis(p_scale);
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elements[2] *= p_scale;
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}
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void Transform2D::scale_basis(const Size2 &p_scale) {
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elements[0][0] *= p_scale.x;
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elements[0][1] *= p_scale.y;
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elements[1][0] *= p_scale.x;
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elements[1][1] *= p_scale.y;
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}
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void Transform2D::translate(real_t p_tx, real_t p_ty) {
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translate(Vector2(p_tx, p_ty));
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}
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void Transform2D::translate(const Vector2 &p_translation) {
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elements[2] += basis_xform(p_translation);
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}
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void Transform2D::orthonormalize() {
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// Gram-Schmidt Process
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Vector2 x = elements[0];
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Vector2 y = elements[1];
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x.normalize();
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y = (y - x * (x.dot(y)));
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y.normalize();
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elements[0] = x;
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elements[1] = y;
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}
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Transform2D Transform2D::orthonormalized() const {
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Transform2D on = *this;
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on.orthonormalize();
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return on;
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}
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bool Transform2D::operator==(const Transform2D &p_transform) const {
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for (int i = 0; i < 3; i++) {
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if (elements[i] != p_transform.elements[i])
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return false;
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}
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return true;
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}
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bool Transform2D::operator!=(const Transform2D &p_transform) const {
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for (int i = 0; i < 3; i++) {
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if (elements[i] != p_transform.elements[i])
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return true;
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}
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return false;
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}
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void Transform2D::operator*=(const Transform2D &p_transform) {
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elements[2] = xform(p_transform.elements[2]);
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real_t x0, x1, y0, y1;
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x0 = tdotx(p_transform.elements[0]);
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x1 = tdoty(p_transform.elements[0]);
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y0 = tdotx(p_transform.elements[1]);
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y1 = tdoty(p_transform.elements[1]);
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elements[0][0] = x0;
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elements[0][1] = x1;
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elements[1][0] = y0;
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elements[1][1] = y1;
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}
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Transform2D Transform2D::operator*(const Transform2D &p_transform) const {
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Transform2D t = *this;
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t *= p_transform;
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return t;
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}
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Transform2D Transform2D::scaled(const Size2 &p_scale) const {
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Transform2D copy = *this;
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copy.scale(p_scale);
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return copy;
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}
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Transform2D Transform2D::basis_scaled(const Size2 &p_scale) const {
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Transform2D copy = *this;
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copy.scale_basis(p_scale);
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return copy;
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}
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Transform2D Transform2D::untranslated() const {
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Transform2D copy = *this;
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copy.elements[2] = Vector2();
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return copy;
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}
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Transform2D Transform2D::translated(const Vector2 &p_offset) const {
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Transform2D copy = *this;
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copy.translate(p_offset);
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return copy;
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}
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Transform2D Transform2D::rotated(real_t p_phi) const {
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Transform2D copy = *this;
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copy.rotate(p_phi);
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return copy;
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}
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real_t Transform2D::basis_determinant() const {
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return elements[0].x * elements[1].y - elements[0].y * elements[1].x;
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}
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Transform2D Transform2D::interpolate_with(const Transform2D &p_transform, real_t p_c) const {
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//extract parameters
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Vector2 p1 = get_origin();
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Vector2 p2 = p_transform.get_origin();
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real_t r1 = get_rotation();
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real_t r2 = p_transform.get_rotation();
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Size2 s1 = get_scale();
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Size2 s2 = p_transform.get_scale();
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//slerp rotation
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Vector2 v1(Math::cos(r1), Math::sin(r1));
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Vector2 v2(Math::cos(r2), Math::sin(r2));
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real_t dot = v1.dot(v2);
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dot = (dot < -1.0) ? -1.0 : ((dot > 1.0) ? 1.0 : dot); //clamp dot to [-1,1]
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Vector2 v;
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if (dot > 0.9995) {
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v = Vector2::linear_interpolate(v1, v2, p_c).normalized(); //linearly interpolate to avoid numerical precision issues
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} else {
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real_t angle = p_c * Math::acos(dot);
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Vector2 v3 = (v2 - v1 * dot).normalized();
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v = v1 * Math::cos(angle) + v3 * Math::sin(angle);
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}
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//construct matrix
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Transform2D res(Math::atan2(v.y, v.x), Vector2::linear_interpolate(p1, p2, p_c));
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res.scale_basis(Vector2::linear_interpolate(s1, s2, p_c));
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return res;
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}
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Transform2D::operator String() const {
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return String(String() + elements[0] + ", " + elements[1] + ", " + elements[2]);
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}
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@ -31,212 +31,10 @@
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#ifndef MATH_2D_H
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#define MATH_2D_H
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#include "math_funcs.h"
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#include "ustring.h"
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#include "vector2.h"
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#include "transform_2d.h"
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/**
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@author Juan Linietsky <reduzio@gmail.com>
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*/
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struct Transform2D;
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struct Rect2 {
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Point2 position;
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Size2 size;
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const Vector2 &get_position() const { return position; }
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void set_position(const Vector2 &p_pos) { position = p_pos; }
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const Vector2 &get_size() const { return size; }
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void set_size(const Vector2 &p_size) { size = p_size; }
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real_t get_area() const { return size.width * size.height; }
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inline bool intersects(const Rect2 &p_rect) const {
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if (position.x >= (p_rect.position.x + p_rect.size.width))
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return false;
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if ((position.x + size.width) <= p_rect.position.x)
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return false;
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if (position.y >= (p_rect.position.y + p_rect.size.height))
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return false;
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if ((position.y + size.height) <= p_rect.position.y)
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return false;
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return true;
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}
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inline real_t distance_to(const Vector2 &p_point) const {
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real_t dist = 0.0;
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bool inside = true;
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if (p_point.x < position.x) {
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real_t d = position.x - p_point.x;
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dist = inside ? d : MIN(dist, d);
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inside = false;
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}
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if (p_point.y < position.y) {
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real_t d = position.y - p_point.y;
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dist = inside ? d : MIN(dist, d);
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inside = false;
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}
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if (p_point.x >= (position.x + size.x)) {
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real_t d = p_point.x - (position.x + size.x);
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dist = inside ? d : MIN(dist, d);
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inside = false;
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}
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if (p_point.y >= (position.y + size.y)) {
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real_t d = p_point.y - (position.y + size.y);
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dist = inside ? d : MIN(dist, d);
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inside = false;
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}
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if (inside)
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return 0;
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else
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return dist;
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}
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_FORCE_INLINE_ bool intersects_transformed(const Transform2D &p_xform, const Rect2 &p_rect) const;
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bool intersects_segment(const Point2 &p_from, const Point2 &p_to, Point2 *r_pos = NULL, Point2 *r_normal = NULL) const;
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inline bool encloses(const Rect2 &p_rect) const {
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return (p_rect.position.x >= position.x) && (p_rect.position.y >= position.y) &&
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((p_rect.position.x + p_rect.size.x) < (position.x + size.x)) &&
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((p_rect.position.y + p_rect.size.y) < (position.y + size.y));
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}
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inline bool has_no_area() const {
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return (size.x <= 0 || size.y <= 0);
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}
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inline Rect2 clip(const Rect2 &p_rect) const { /// return a clipped rect
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Rect2 new_rect = p_rect;
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if (!intersects(new_rect))
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return Rect2();
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new_rect.position.x = MAX(p_rect.position.x, position.x);
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new_rect.position.y = MAX(p_rect.position.y, position.y);
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Point2 p_rect_end = p_rect.position + p_rect.size;
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Point2 end = position + size;
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new_rect.size.x = MIN(p_rect_end.x, end.x) - new_rect.position.x;
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new_rect.size.y = MIN(p_rect_end.y, end.y) - new_rect.position.y;
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return new_rect;
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}
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inline Rect2 merge(const Rect2 &p_rect) const { ///< return a merged rect
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Rect2 new_rect;
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new_rect.position.x = MIN(p_rect.position.x, position.x);
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new_rect.position.y = MIN(p_rect.position.y, position.y);
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new_rect.size.x = MAX(p_rect.position.x + p_rect.size.x, position.x + size.x);
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new_rect.size.y = MAX(p_rect.position.y + p_rect.size.y, position.y + size.y);
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new_rect.size = new_rect.size - new_rect.position; //make relative again
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return new_rect;
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};
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inline bool has_point(const Point2 &p_point) const {
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if (p_point.x < position.x)
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return false;
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if (p_point.y < position.y)
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return false;
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if (p_point.x >= (position.x + size.x))
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return false;
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if (p_point.y >= (position.y + size.y))
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return false;
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return true;
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}
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inline bool no_area() const { return (size.width <= 0 || size.height <= 0); }
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bool operator==(const Rect2 &p_rect) const { return position == p_rect.position && size == p_rect.size; }
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bool operator!=(const Rect2 &p_rect) const { return position != p_rect.position || size != p_rect.size; }
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inline Rect2 grow(real_t p_by) const {
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Rect2 g = *this;
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g.position.x -= p_by;
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g.position.y -= p_by;
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g.size.width += p_by * 2;
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g.size.height += p_by * 2;
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return g;
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}
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inline Rect2 grow_margin(Margin p_margin, real_t p_amount) const {
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Rect2 g = *this;
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g = g.grow_individual((MARGIN_LEFT == p_margin) ? p_amount : 0,
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(MARGIN_TOP == p_margin) ? p_amount : 0,
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(MARGIN_RIGHT == p_margin) ? p_amount : 0,
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(MARGIN_BOTTOM == p_margin) ? p_amount : 0);
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return g;
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}
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inline Rect2 grow_individual(real_t p_left, real_t p_top, real_t p_right, real_t p_bottom) const {
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Rect2 g = *this;
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g.position.x -= p_left;
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g.position.y -= p_top;
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g.size.width += p_left + p_right;
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g.size.height += p_top + p_bottom;
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return g;
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}
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inline Rect2 expand(const Vector2 &p_vector) const {
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Rect2 r = *this;
|
||||
r.expand_to(p_vector);
|
||||
return r;
|
||||
}
|
||||
|
||||
inline void expand_to(const Vector2 &p_vector) { //in place function for speed
|
||||
|
||||
Vector2 begin = position;
|
||||
Vector2 end = position + size;
|
||||
|
||||
if (p_vector.x < begin.x)
|
||||
begin.x = p_vector.x;
|
||||
if (p_vector.y < begin.y)
|
||||
begin.y = p_vector.y;
|
||||
|
||||
if (p_vector.x > end.x)
|
||||
end.x = p_vector.x;
|
||||
if (p_vector.y > end.y)
|
||||
end.y = p_vector.y;
|
||||
|
||||
position = begin;
|
||||
size = end - begin;
|
||||
}
|
||||
|
||||
inline Rect2 abs() const {
|
||||
|
||||
return Rect2(Point2(position.x + MIN(size.x, 0), position.y + MIN(size.y, 0)), size.abs());
|
||||
}
|
||||
|
||||
operator String() const { return String(position) + ", " + String(size); }
|
||||
|
||||
Rect2() {}
|
||||
Rect2(real_t p_x, real_t p_y, real_t p_width, real_t p_height) :
|
||||
position(Point2(p_x, p_y)),
|
||||
size(Size2(p_width, p_height)) {
|
||||
}
|
||||
Rect2(const Point2 &p_pos, const Size2 &p_size) :
|
||||
position(p_pos),
|
||||
size(p_size) {
|
||||
}
|
||||
};
|
||||
|
||||
/* INTEGER STUFF */
|
||||
|
||||
struct Point2i {
|
||||
|
|
@ -435,320 +233,4 @@ struct Rect2i {
|
|||
}
|
||||
};
|
||||
|
||||
struct Transform2D {
|
||||
// Warning #1: basis of Transform2D is stored differently from Basis. In terms of elements array, the basis matrix looks like "on paper":
|
||||
// M = (elements[0][0] elements[1][0])
|
||||
// (elements[0][1] elements[1][1])
|
||||
// This is such that the columns, which can be interpreted as basis vectors of the coordinate system "painted" on the object, can be accessed as elements[i].
|
||||
// Note that this is the opposite of the indices in mathematical texts, meaning: $M_{12}$ in a math book corresponds to elements[1][0] here.
|
||||
// This requires additional care when working with explicit indices.
|
||||
// See https://en.wikipedia.org/wiki/Row-_and_column-major_order for further reading.
|
||||
|
||||
// Warning #2: 2D be aware that unlike 3D code, 2D code uses a left-handed coordinate system: Y-axis points down,
|
||||
// and angle is measure from +X to +Y in a clockwise-fashion.
|
||||
|
||||
Vector2 elements[3];
|
||||
|
||||
_FORCE_INLINE_ real_t tdotx(const Vector2 &v) const { return elements[0][0] * v.x + elements[1][0] * v.y; }
|
||||
_FORCE_INLINE_ real_t tdoty(const Vector2 &v) const { return elements[0][1] * v.x + elements[1][1] * v.y; }
|
||||
|
||||
const Vector2 &operator[](int p_idx) const { return elements[p_idx]; }
|
||||
Vector2 &operator[](int p_idx) { return elements[p_idx]; }
|
||||
|
||||
_FORCE_INLINE_ Vector2 get_axis(int p_axis) const {
|
||||
ERR_FAIL_INDEX_V(p_axis, 3, Vector2());
|
||||
return elements[p_axis];
|
||||
}
|
||||
_FORCE_INLINE_ void set_axis(int p_axis, const Vector2 &p_vec) {
|
||||
ERR_FAIL_INDEX(p_axis, 3);
|
||||
elements[p_axis] = p_vec;
|
||||
}
|
||||
|
||||
void invert();
|
||||
Transform2D inverse() const;
|
||||
|
||||
void affine_invert();
|
||||
Transform2D affine_inverse() const;
|
||||
|
||||
void set_rotation(real_t p_rot);
|
||||
real_t get_rotation() const;
|
||||
_FORCE_INLINE_ void set_rotation_and_scale(real_t p_rot, const Size2 &p_scale);
|
||||
void rotate(real_t p_phi);
|
||||
|
||||
void scale(const Size2 &p_scale);
|
||||
void scale_basis(const Size2 &p_scale);
|
||||
void translate(real_t p_tx, real_t p_ty);
|
||||
void translate(const Vector2 &p_translation);
|
||||
|
||||
real_t basis_determinant() const;
|
||||
|
||||
Size2 get_scale() const;
|
||||
|
||||
_FORCE_INLINE_ const Vector2 &get_origin() const { return elements[2]; }
|
||||
_FORCE_INLINE_ void set_origin(const Vector2 &p_origin) { elements[2] = p_origin; }
|
||||
|
||||
Transform2D scaled(const Size2 &p_scale) const;
|
||||
Transform2D basis_scaled(const Size2 &p_scale) const;
|
||||
Transform2D translated(const Vector2 &p_offset) const;
|
||||
Transform2D rotated(real_t p_phi) const;
|
||||
|
||||
Transform2D untranslated() const;
|
||||
|
||||
void orthonormalize();
|
||||
Transform2D orthonormalized() const;
|
||||
|
||||
bool operator==(const Transform2D &p_transform) const;
|
||||
bool operator!=(const Transform2D &p_transform) const;
|
||||
|
||||
void operator*=(const Transform2D &p_transform);
|
||||
Transform2D operator*(const Transform2D &p_transform) const;
|
||||
|
||||
Transform2D interpolate_with(const Transform2D &p_transform, real_t p_c) const;
|
||||
|
||||
_FORCE_INLINE_ Vector2 basis_xform(const Vector2 &p_vec) const;
|
||||
_FORCE_INLINE_ Vector2 basis_xform_inv(const Vector2 &p_vec) const;
|
||||
_FORCE_INLINE_ Vector2 xform(const Vector2 &p_vec) const;
|
||||
_FORCE_INLINE_ Vector2 xform_inv(const Vector2 &p_vec) const;
|
||||
_FORCE_INLINE_ Rect2 xform(const Rect2 &p_rect) const;
|
||||
_FORCE_INLINE_ Rect2 xform_inv(const Rect2 &p_rect) const;
|
||||
|
||||
operator String() const;
|
||||
|
||||
Transform2D(real_t xx, real_t xy, real_t yx, real_t yy, real_t ox, real_t oy) {
|
||||
|
||||
elements[0][0] = xx;
|
||||
elements[0][1] = xy;
|
||||
elements[1][0] = yx;
|
||||
elements[1][1] = yy;
|
||||
elements[2][0] = ox;
|
||||
elements[2][1] = oy;
|
||||
}
|
||||
|
||||
Transform2D(real_t p_rot, const Vector2 &p_pos);
|
||||
Transform2D() {
|
||||
elements[0][0] = 1.0;
|
||||
elements[1][1] = 1.0;
|
||||
}
|
||||
};
|
||||
|
||||
bool Rect2::intersects_transformed(const Transform2D &p_xform, const Rect2 &p_rect) const {
|
||||
|
||||
//SAT intersection between local and transformed rect2
|
||||
|
||||
Vector2 xf_points[4] = {
|
||||
p_xform.xform(p_rect.position),
|
||||
p_xform.xform(Vector2(p_rect.position.x + p_rect.size.x, p_rect.position.y)),
|
||||
p_xform.xform(Vector2(p_rect.position.x, p_rect.position.y + p_rect.size.y)),
|
||||
p_xform.xform(Vector2(p_rect.position.x + p_rect.size.x, p_rect.position.y + p_rect.size.y)),
|
||||
};
|
||||
|
||||
real_t low_limit;
|
||||
|
||||
//base rect2 first (faster)
|
||||
|
||||
if (xf_points[0].y > position.y)
|
||||
goto next1;
|
||||
if (xf_points[1].y > position.y)
|
||||
goto next1;
|
||||
if (xf_points[2].y > position.y)
|
||||
goto next1;
|
||||
if (xf_points[3].y > position.y)
|
||||
goto next1;
|
||||
|
||||
return false;
|
||||
|
||||
next1:
|
||||
|
||||
low_limit = position.y + size.y;
|
||||
|
||||
if (xf_points[0].y < low_limit)
|
||||
goto next2;
|
||||
if (xf_points[1].y < low_limit)
|
||||
goto next2;
|
||||
if (xf_points[2].y < low_limit)
|
||||
goto next2;
|
||||
if (xf_points[3].y < low_limit)
|
||||
goto next2;
|
||||
|
||||
return false;
|
||||
|
||||
next2:
|
||||
|
||||
if (xf_points[0].x > position.x)
|
||||
goto next3;
|
||||
if (xf_points[1].x > position.x)
|
||||
goto next3;
|
||||
if (xf_points[2].x > position.x)
|
||||
goto next3;
|
||||
if (xf_points[3].x > position.x)
|
||||
goto next3;
|
||||
|
||||
return false;
|
||||
|
||||
next3:
|
||||
|
||||
low_limit = position.x + size.x;
|
||||
|
||||
if (xf_points[0].x < low_limit)
|
||||
goto next4;
|
||||
if (xf_points[1].x < low_limit)
|
||||
goto next4;
|
||||
if (xf_points[2].x < low_limit)
|
||||
goto next4;
|
||||
if (xf_points[3].x < low_limit)
|
||||
goto next4;
|
||||
|
||||
return false;
|
||||
|
||||
next4:
|
||||
|
||||
Vector2 xf_points2[4] = {
|
||||
position,
|
||||
Vector2(position.x + size.x, position.y),
|
||||
Vector2(position.x, position.y + size.y),
|
||||
Vector2(position.x + size.x, position.y + size.y),
|
||||
};
|
||||
|
||||
real_t maxa = p_xform.elements[0].dot(xf_points2[0]);
|
||||
real_t mina = maxa;
|
||||
|
||||
real_t dp = p_xform.elements[0].dot(xf_points2[1]);
|
||||
maxa = MAX(dp, maxa);
|
||||
mina = MIN(dp, mina);
|
||||
|
||||
dp = p_xform.elements[0].dot(xf_points2[2]);
|
||||
maxa = MAX(dp, maxa);
|
||||
mina = MIN(dp, mina);
|
||||
|
||||
dp = p_xform.elements[0].dot(xf_points2[3]);
|
||||
maxa = MAX(dp, maxa);
|
||||
mina = MIN(dp, mina);
|
||||
|
||||
real_t maxb = p_xform.elements[0].dot(xf_points[0]);
|
||||
real_t minb = maxb;
|
||||
|
||||
dp = p_xform.elements[0].dot(xf_points[1]);
|
||||
maxb = MAX(dp, maxb);
|
||||
minb = MIN(dp, minb);
|
||||
|
||||
dp = p_xform.elements[0].dot(xf_points[2]);
|
||||
maxb = MAX(dp, maxb);
|
||||
minb = MIN(dp, minb);
|
||||
|
||||
dp = p_xform.elements[0].dot(xf_points[3]);
|
||||
maxb = MAX(dp, maxb);
|
||||
minb = MIN(dp, minb);
|
||||
|
||||
if (mina > maxb)
|
||||
return false;
|
||||
if (minb > maxa)
|
||||
return false;
|
||||
|
||||
maxa = p_xform.elements[1].dot(xf_points2[0]);
|
||||
mina = maxa;
|
||||
|
||||
dp = p_xform.elements[1].dot(xf_points2[1]);
|
||||
maxa = MAX(dp, maxa);
|
||||
mina = MIN(dp, mina);
|
||||
|
||||
dp = p_xform.elements[1].dot(xf_points2[2]);
|
||||
maxa = MAX(dp, maxa);
|
||||
mina = MIN(dp, mina);
|
||||
|
||||
dp = p_xform.elements[1].dot(xf_points2[3]);
|
||||
maxa = MAX(dp, maxa);
|
||||
mina = MIN(dp, mina);
|
||||
|
||||
maxb = p_xform.elements[1].dot(xf_points[0]);
|
||||
minb = maxb;
|
||||
|
||||
dp = p_xform.elements[1].dot(xf_points[1]);
|
||||
maxb = MAX(dp, maxb);
|
||||
minb = MIN(dp, minb);
|
||||
|
||||
dp = p_xform.elements[1].dot(xf_points[2]);
|
||||
maxb = MAX(dp, maxb);
|
||||
minb = MIN(dp, minb);
|
||||
|
||||
dp = p_xform.elements[1].dot(xf_points[3]);
|
||||
maxb = MAX(dp, maxb);
|
||||
minb = MIN(dp, minb);
|
||||
|
||||
if (mina > maxb)
|
||||
return false;
|
||||
if (minb > maxa)
|
||||
return false;
|
||||
|
||||
return true;
|
||||
}
|
||||
|
||||
Vector2 Transform2D::basis_xform(const Vector2 &p_vec) const {
|
||||
|
||||
return Vector2(
|
||||
tdotx(p_vec),
|
||||
tdoty(p_vec));
|
||||
}
|
||||
|
||||
Vector2 Transform2D::basis_xform_inv(const Vector2 &p_vec) const {
|
||||
|
||||
return Vector2(
|
||||
elements[0].dot(p_vec),
|
||||
elements[1].dot(p_vec));
|
||||
}
|
||||
|
||||
Vector2 Transform2D::xform(const Vector2 &p_vec) const {
|
||||
|
||||
return Vector2(
|
||||
tdotx(p_vec),
|
||||
tdoty(p_vec)) +
|
||||
elements[2];
|
||||
}
|
||||
Vector2 Transform2D::xform_inv(const Vector2 &p_vec) const {
|
||||
|
||||
Vector2 v = p_vec - elements[2];
|
||||
|
||||
return Vector2(
|
||||
elements[0].dot(v),
|
||||
elements[1].dot(v));
|
||||
}
|
||||
Rect2 Transform2D::xform(const Rect2 &p_rect) const {
|
||||
|
||||
Vector2 x = elements[0] * p_rect.size.x;
|
||||
Vector2 y = elements[1] * p_rect.size.y;
|
||||
Vector2 pos = xform(p_rect.position);
|
||||
|
||||
Rect2 new_rect;
|
||||
new_rect.position = pos;
|
||||
new_rect.expand_to(pos + x);
|
||||
new_rect.expand_to(pos + y);
|
||||
new_rect.expand_to(pos + x + y);
|
||||
return new_rect;
|
||||
}
|
||||
|
||||
void Transform2D::set_rotation_and_scale(real_t p_rot, const Size2 &p_scale) {
|
||||
|
||||
elements[0][0] = Math::cos(p_rot) * p_scale.x;
|
||||
elements[1][1] = Math::cos(p_rot) * p_scale.y;
|
||||
elements[1][0] = -Math::sin(p_rot) * p_scale.y;
|
||||
elements[0][1] = Math::sin(p_rot) * p_scale.x;
|
||||
}
|
||||
|
||||
Rect2 Transform2D::xform_inv(const Rect2 &p_rect) const {
|
||||
|
||||
Vector2 ends[4] = {
|
||||
xform_inv(p_rect.position),
|
||||
xform_inv(Vector2(p_rect.position.x, p_rect.position.y + p_rect.size.y)),
|
||||
xform_inv(Vector2(p_rect.position.x + p_rect.size.x, p_rect.position.y + p_rect.size.y)),
|
||||
xform_inv(Vector2(p_rect.position.x + p_rect.size.x, p_rect.position.y))
|
||||
};
|
||||
|
||||
Rect2 new_rect;
|
||||
new_rect.position = ends[0];
|
||||
new_rect.expand_to(ends[1]);
|
||||
new_rect.expand_to(ends[2]);
|
||||
new_rect.expand_to(ends[3]);
|
||||
|
||||
return new_rect;
|
||||
}
|
||||
|
||||
#endif
|
||||
|
|
|
|||
240
core/math/rect2.cpp
Normal file
240
core/math/rect2.cpp
Normal file
|
|
@ -0,0 +1,240 @@
|
|||
/*************************************************************************/
|
||||
/* rect2.cpp */
|
||||
/*************************************************************************/
|
||||
/* This file is part of: */
|
||||
/* GODOT ENGINE */
|
||||
/* https://godotengine.org */
|
||||
/*************************************************************************/
|
||||
/* Copyright (c) 2007-2018 Juan Linietsky, Ariel Manzur. */
|
||||
/* Copyright (c) 2014-2018 Godot Engine contributors (cf. AUTHORS.md) */
|
||||
/* */
|
||||
/* Permission is hereby granted, free of charge, to any person obtaining */
|
||||
/* a copy of this software and associated documentation files (the */
|
||||
/* "Software"), to deal in the Software without restriction, including */
|
||||
/* without limitation the rights to use, copy, modify, merge, publish, */
|
||||
/* distribute, sublicense, and/or sell copies of the Software, and to */
|
||||
/* permit persons to whom the Software is furnished to do so, subject to */
|
||||
/* the following conditions: */
|
||||
/* */
|
||||
/* The above copyright notice and this permission notice shall be */
|
||||
/* included in all copies or substantial portions of the Software. */
|
||||
/* */
|
||||
/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, */
|
||||
/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF */
|
||||
/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
|
||||
/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY */
|
||||
/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, */
|
||||
/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE */
|
||||
/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */
|
||||
/*************************************************************************/
|
||||
|
||||
#include "transform_2d.h" // Includes rect2.h but Rect2 needs Transform2D
|
||||
|
||||
bool Rect2::intersects_segment(const Point2 &p_from, const Point2 &p_to, Point2 *r_pos, Point2 *r_normal) const {
|
||||
|
||||
real_t min = 0, max = 1;
|
||||
int axis = 0;
|
||||
real_t sign = 0;
|
||||
|
||||
for (int i = 0; i < 2; i++) {
|
||||
real_t seg_from = p_from[i];
|
||||
real_t seg_to = p_to[i];
|
||||
real_t box_begin = position[i];
|
||||
real_t box_end = box_begin + size[i];
|
||||
real_t cmin, cmax;
|
||||
real_t csign;
|
||||
|
||||
if (seg_from < seg_to) {
|
||||
|
||||
if (seg_from > box_end || seg_to < box_begin)
|
||||
return false;
|
||||
real_t length = seg_to - seg_from;
|
||||
cmin = (seg_from < box_begin) ? ((box_begin - seg_from) / length) : 0;
|
||||
cmax = (seg_to > box_end) ? ((box_end - seg_from) / length) : 1;
|
||||
csign = -1.0;
|
||||
|
||||
} else {
|
||||
|
||||
if (seg_to > box_end || seg_from < box_begin)
|
||||
return false;
|
||||
real_t length = seg_to - seg_from;
|
||||
cmin = (seg_from > box_end) ? (box_end - seg_from) / length : 0;
|
||||
cmax = (seg_to < box_begin) ? (box_begin - seg_from) / length : 1;
|
||||
csign = 1.0;
|
||||
}
|
||||
|
||||
if (cmin > min) {
|
||||
min = cmin;
|
||||
axis = i;
|
||||
sign = csign;
|
||||
}
|
||||
if (cmax < max)
|
||||
max = cmax;
|
||||
if (max < min)
|
||||
return false;
|
||||
}
|
||||
|
||||
Vector2 rel = p_to - p_from;
|
||||
|
||||
if (r_normal) {
|
||||
Vector2 normal;
|
||||
normal[axis] = sign;
|
||||
*r_normal = normal;
|
||||
}
|
||||
|
||||
if (r_pos)
|
||||
*r_pos = p_from + rel * min;
|
||||
|
||||
return true;
|
||||
}
|
||||
|
||||
bool Rect2::intersects_transformed(const Transform2D &p_xform, const Rect2 &p_rect) const {
|
||||
|
||||
//SAT intersection between local and transformed rect2
|
||||
|
||||
Vector2 xf_points[4] = {
|
||||
p_xform.xform(p_rect.position),
|
||||
p_xform.xform(Vector2(p_rect.position.x + p_rect.size.x, p_rect.position.y)),
|
||||
p_xform.xform(Vector2(p_rect.position.x, p_rect.position.y + p_rect.size.y)),
|
||||
p_xform.xform(Vector2(p_rect.position.x + p_rect.size.x, p_rect.position.y + p_rect.size.y)),
|
||||
};
|
||||
|
||||
real_t low_limit;
|
||||
|
||||
//base rect2 first (faster)
|
||||
|
||||
if (xf_points[0].y > position.y)
|
||||
goto next1;
|
||||
if (xf_points[1].y > position.y)
|
||||
goto next1;
|
||||
if (xf_points[2].y > position.y)
|
||||
goto next1;
|
||||
if (xf_points[3].y > position.y)
|
||||
goto next1;
|
||||
|
||||
return false;
|
||||
|
||||
next1:
|
||||
|
||||
low_limit = position.y + size.y;
|
||||
|
||||
if (xf_points[0].y < low_limit)
|
||||
goto next2;
|
||||
if (xf_points[1].y < low_limit)
|
||||
goto next2;
|
||||
if (xf_points[2].y < low_limit)
|
||||
goto next2;
|
||||
if (xf_points[3].y < low_limit)
|
||||
goto next2;
|
||||
|
||||
return false;
|
||||
|
||||
next2:
|
||||
|
||||
if (xf_points[0].x > position.x)
|
||||
goto next3;
|
||||
if (xf_points[1].x > position.x)
|
||||
goto next3;
|
||||
if (xf_points[2].x > position.x)
|
||||
goto next3;
|
||||
if (xf_points[3].x > position.x)
|
||||
goto next3;
|
||||
|
||||
return false;
|
||||
|
||||
next3:
|
||||
|
||||
low_limit = position.x + size.x;
|
||||
|
||||
if (xf_points[0].x < low_limit)
|
||||
goto next4;
|
||||
if (xf_points[1].x < low_limit)
|
||||
goto next4;
|
||||
if (xf_points[2].x < low_limit)
|
||||
goto next4;
|
||||
if (xf_points[3].x < low_limit)
|
||||
goto next4;
|
||||
|
||||
return false;
|
||||
|
||||
next4:
|
||||
|
||||
Vector2 xf_points2[4] = {
|
||||
position,
|
||||
Vector2(position.x + size.x, position.y),
|
||||
Vector2(position.x, position.y + size.y),
|
||||
Vector2(position.x + size.x, position.y + size.y),
|
||||
};
|
||||
|
||||
real_t maxa = p_xform.elements[0].dot(xf_points2[0]);
|
||||
real_t mina = maxa;
|
||||
|
||||
real_t dp = p_xform.elements[0].dot(xf_points2[1]);
|
||||
maxa = MAX(dp, maxa);
|
||||
mina = MIN(dp, mina);
|
||||
|
||||
dp = p_xform.elements[0].dot(xf_points2[2]);
|
||||
maxa = MAX(dp, maxa);
|
||||
mina = MIN(dp, mina);
|
||||
|
||||
dp = p_xform.elements[0].dot(xf_points2[3]);
|
||||
maxa = MAX(dp, maxa);
|
||||
mina = MIN(dp, mina);
|
||||
|
||||
real_t maxb = p_xform.elements[0].dot(xf_points[0]);
|
||||
real_t minb = maxb;
|
||||
|
||||
dp = p_xform.elements[0].dot(xf_points[1]);
|
||||
maxb = MAX(dp, maxb);
|
||||
minb = MIN(dp, minb);
|
||||
|
||||
dp = p_xform.elements[0].dot(xf_points[2]);
|
||||
maxb = MAX(dp, maxb);
|
||||
minb = MIN(dp, minb);
|
||||
|
||||
dp = p_xform.elements[0].dot(xf_points[3]);
|
||||
maxb = MAX(dp, maxb);
|
||||
minb = MIN(dp, minb);
|
||||
|
||||
if (mina > maxb)
|
||||
return false;
|
||||
if (minb > maxa)
|
||||
return false;
|
||||
|
||||
maxa = p_xform.elements[1].dot(xf_points2[0]);
|
||||
mina = maxa;
|
||||
|
||||
dp = p_xform.elements[1].dot(xf_points2[1]);
|
||||
maxa = MAX(dp, maxa);
|
||||
mina = MIN(dp, mina);
|
||||
|
||||
dp = p_xform.elements[1].dot(xf_points2[2]);
|
||||
maxa = MAX(dp, maxa);
|
||||
mina = MIN(dp, mina);
|
||||
|
||||
dp = p_xform.elements[1].dot(xf_points2[3]);
|
||||
maxa = MAX(dp, maxa);
|
||||
mina = MIN(dp, mina);
|
||||
|
||||
maxb = p_xform.elements[1].dot(xf_points[0]);
|
||||
minb = maxb;
|
||||
|
||||
dp = p_xform.elements[1].dot(xf_points[1]);
|
||||
maxb = MAX(dp, maxb);
|
||||
minb = MIN(dp, minb);
|
||||
|
||||
dp = p_xform.elements[1].dot(xf_points[2]);
|
||||
maxb = MAX(dp, maxb);
|
||||
minb = MIN(dp, minb);
|
||||
|
||||
dp = p_xform.elements[1].dot(xf_points[3]);
|
||||
maxb = MAX(dp, maxb);
|
||||
minb = MIN(dp, minb);
|
||||
|
||||
if (mina > maxb)
|
||||
return false;
|
||||
if (minb > maxa)
|
||||
return false;
|
||||
|
||||
return true;
|
||||
}
|
||||
236
core/math/rect2.h
Normal file
236
core/math/rect2.h
Normal file
|
|
@ -0,0 +1,236 @@
|
|||
/*************************************************************************/
|
||||
/* rect2.h */
|
||||
/*************************************************************************/
|
||||
/* This file is part of: */
|
||||
/* GODOT ENGINE */
|
||||
/* https://godotengine.org */
|
||||
/*************************************************************************/
|
||||
/* Copyright (c) 2007-2018 Juan Linietsky, Ariel Manzur. */
|
||||
/* Copyright (c) 2014-2018 Godot Engine contributors (cf. AUTHORS.md) */
|
||||
/* */
|
||||
/* Permission is hereby granted, free of charge, to any person obtaining */
|
||||
/* a copy of this software and associated documentation files (the */
|
||||
/* "Software"), to deal in the Software without restriction, including */
|
||||
/* without limitation the rights to use, copy, modify, merge, publish, */
|
||||
/* distribute, sublicense, and/or sell copies of the Software, and to */
|
||||
/* permit persons to whom the Software is furnished to do so, subject to */
|
||||
/* the following conditions: */
|
||||
/* */
|
||||
/* The above copyright notice and this permission notice shall be */
|
||||
/* included in all copies or substantial portions of the Software. */
|
||||
/* */
|
||||
/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, */
|
||||
/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF */
|
||||
/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
|
||||
/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY */
|
||||
/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, */
|
||||
/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE */
|
||||
/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */
|
||||
/*************************************************************************/
|
||||
|
||||
#ifndef RECT2_H
|
||||
#define RECT2_H
|
||||
|
||||
#include "vector2.h" // also includes math_funcs and ustring
|
||||
|
||||
struct Transform2D;
|
||||
|
||||
struct Rect2 {
|
||||
|
||||
Point2 position;
|
||||
Size2 size;
|
||||
|
||||
const Vector2 &get_position() const { return position; }
|
||||
void set_position(const Vector2 &p_pos) { position = p_pos; }
|
||||
const Vector2 &get_size() const { return size; }
|
||||
void set_size(const Vector2 &p_size) { size = p_size; }
|
||||
|
||||
real_t get_area() const { return size.width * size.height; }
|
||||
|
||||
inline bool intersects(const Rect2 &p_rect) const {
|
||||
if (position.x >= (p_rect.position.x + p_rect.size.width))
|
||||
return false;
|
||||
if ((position.x + size.width) <= p_rect.position.x)
|
||||
return false;
|
||||
if (position.y >= (p_rect.position.y + p_rect.size.height))
|
||||
return false;
|
||||
if ((position.y + size.height) <= p_rect.position.y)
|
||||
return false;
|
||||
|
||||
return true;
|
||||
}
|
||||
|
||||
inline real_t distance_to(const Vector2 &p_point) const {
|
||||
|
||||
real_t dist = 0.0;
|
||||
bool inside = true;
|
||||
|
||||
if (p_point.x < position.x) {
|
||||
real_t d = position.x - p_point.x;
|
||||
dist = inside ? d : MIN(dist, d);
|
||||
inside = false;
|
||||
}
|
||||
if (p_point.y < position.y) {
|
||||
real_t d = position.y - p_point.y;
|
||||
dist = inside ? d : MIN(dist, d);
|
||||
inside = false;
|
||||
}
|
||||
if (p_point.x >= (position.x + size.x)) {
|
||||
real_t d = p_point.x - (position.x + size.x);
|
||||
dist = inside ? d : MIN(dist, d);
|
||||
inside = false;
|
||||
}
|
||||
if (p_point.y >= (position.y + size.y)) {
|
||||
real_t d = p_point.y - (position.y + size.y);
|
||||
dist = inside ? d : MIN(dist, d);
|
||||
inside = false;
|
||||
}
|
||||
|
||||
if (inside)
|
||||
return 0;
|
||||
else
|
||||
return dist;
|
||||
}
|
||||
|
||||
bool intersects_transformed(const Transform2D &p_xform, const Rect2 &p_rect) const;
|
||||
|
||||
bool intersects_segment(const Point2 &p_from, const Point2 &p_to, Point2 *r_pos = NULL, Point2 *r_normal = NULL) const;
|
||||
|
||||
inline bool encloses(const Rect2 &p_rect) const {
|
||||
|
||||
return (p_rect.position.x >= position.x) && (p_rect.position.y >= position.y) &&
|
||||
((p_rect.position.x + p_rect.size.x) < (position.x + size.x)) &&
|
||||
((p_rect.position.y + p_rect.size.y) < (position.y + size.y));
|
||||
}
|
||||
|
||||
inline bool has_no_area() const {
|
||||
|
||||
return (size.x <= 0 || size.y <= 0);
|
||||
}
|
||||
inline Rect2 clip(const Rect2 &p_rect) const { /// return a clipped rect
|
||||
|
||||
Rect2 new_rect = p_rect;
|
||||
|
||||
if (!intersects(new_rect))
|
||||
return Rect2();
|
||||
|
||||
new_rect.position.x = MAX(p_rect.position.x, position.x);
|
||||
new_rect.position.y = MAX(p_rect.position.y, position.y);
|
||||
|
||||
Point2 p_rect_end = p_rect.position + p_rect.size;
|
||||
Point2 end = position + size;
|
||||
|
||||
new_rect.size.x = MIN(p_rect_end.x, end.x) - new_rect.position.x;
|
||||
new_rect.size.y = MIN(p_rect_end.y, end.y) - new_rect.position.y;
|
||||
|
||||
return new_rect;
|
||||
}
|
||||
|
||||
inline Rect2 merge(const Rect2 &p_rect) const { ///< return a merged rect
|
||||
|
||||
Rect2 new_rect;
|
||||
|
||||
new_rect.position.x = MIN(p_rect.position.x, position.x);
|
||||
new_rect.position.y = MIN(p_rect.position.y, position.y);
|
||||
|
||||
new_rect.size.x = MAX(p_rect.position.x + p_rect.size.x, position.x + size.x);
|
||||
new_rect.size.y = MAX(p_rect.position.y + p_rect.size.y, position.y + size.y);
|
||||
|
||||
new_rect.size = new_rect.size - new_rect.position; //make relative again
|
||||
|
||||
return new_rect;
|
||||
};
|
||||
inline bool has_point(const Point2 &p_point) const {
|
||||
if (p_point.x < position.x)
|
||||
return false;
|
||||
if (p_point.y < position.y)
|
||||
return false;
|
||||
|
||||
if (p_point.x >= (position.x + size.x))
|
||||
return false;
|
||||
if (p_point.y >= (position.y + size.y))
|
||||
return false;
|
||||
|
||||
return true;
|
||||
}
|
||||
|
||||
inline bool no_area() const { return (size.width <= 0 || size.height <= 0); }
|
||||
|
||||
bool operator==(const Rect2 &p_rect) const { return position == p_rect.position && size == p_rect.size; }
|
||||
bool operator!=(const Rect2 &p_rect) const { return position != p_rect.position || size != p_rect.size; }
|
||||
|
||||
inline Rect2 grow(real_t p_by) const {
|
||||
|
||||
Rect2 g = *this;
|
||||
g.position.x -= p_by;
|
||||
g.position.y -= p_by;
|
||||
g.size.width += p_by * 2;
|
||||
g.size.height += p_by * 2;
|
||||
return g;
|
||||
}
|
||||
|
||||
inline Rect2 grow_margin(Margin p_margin, real_t p_amount) const {
|
||||
Rect2 g = *this;
|
||||
g = g.grow_individual((MARGIN_LEFT == p_margin) ? p_amount : 0,
|
||||
(MARGIN_TOP == p_margin) ? p_amount : 0,
|
||||
(MARGIN_RIGHT == p_margin) ? p_amount : 0,
|
||||
(MARGIN_BOTTOM == p_margin) ? p_amount : 0);
|
||||
return g;
|
||||
}
|
||||
|
||||
inline Rect2 grow_individual(real_t p_left, real_t p_top, real_t p_right, real_t p_bottom) const {
|
||||
|
||||
Rect2 g = *this;
|
||||
g.position.x -= p_left;
|
||||
g.position.y -= p_top;
|
||||
g.size.width += p_left + p_right;
|
||||
g.size.height += p_top + p_bottom;
|
||||
|
||||
return g;
|
||||
}
|
||||
|
||||
inline Rect2 expand(const Vector2 &p_vector) const {
|
||||
|
||||
Rect2 r = *this;
|
||||
r.expand_to(p_vector);
|
||||
return r;
|
||||
}
|
||||
|
||||
inline void expand_to(const Vector2 &p_vector) { //in place function for speed
|
||||
|
||||
Vector2 begin = position;
|
||||
Vector2 end = position + size;
|
||||
|
||||
if (p_vector.x < begin.x)
|
||||
begin.x = p_vector.x;
|
||||
if (p_vector.y < begin.y)
|
||||
begin.y = p_vector.y;
|
||||
|
||||
if (p_vector.x > end.x)
|
||||
end.x = p_vector.x;
|
||||
if (p_vector.y > end.y)
|
||||
end.y = p_vector.y;
|
||||
|
||||
position = begin;
|
||||
size = end - begin;
|
||||
}
|
||||
|
||||
inline Rect2 abs() const {
|
||||
|
||||
return Rect2(Point2(position.x + MIN(size.x, 0), position.y + MIN(size.y, 0)), size.abs());
|
||||
}
|
||||
|
||||
operator String() const { return String(position) + ", " + String(size); }
|
||||
|
||||
Rect2() {}
|
||||
Rect2(real_t p_x, real_t p_y, real_t p_width, real_t p_height) :
|
||||
position(Point2(p_x, p_y)),
|
||||
size(Size2(p_width, p_height)) {
|
||||
}
|
||||
Rect2(const Point2 &p_pos, const Size2 &p_size) :
|
||||
position(p_pos),
|
||||
size(p_size) {
|
||||
}
|
||||
};
|
||||
|
||||
#endif // RECT2_H
|
||||
272
core/math/transform_2d.cpp
Normal file
272
core/math/transform_2d.cpp
Normal file
|
|
@ -0,0 +1,272 @@
|
|||
/*************************************************************************/
|
||||
/* transform_2d.cpp */
|
||||
/*************************************************************************/
|
||||
/* This file is part of: */
|
||||
/* GODOT ENGINE */
|
||||
/* https://godotengine.org */
|
||||
/*************************************************************************/
|
||||
/* Copyright (c) 2007-2018 Juan Linietsky, Ariel Manzur. */
|
||||
/* Copyright (c) 2014-2018 Godot Engine contributors (cf. AUTHORS.md) */
|
||||
/* */
|
||||
/* Permission is hereby granted, free of charge, to any person obtaining */
|
||||
/* a copy of this software and associated documentation files (the */
|
||||
/* "Software"), to deal in the Software without restriction, including */
|
||||
/* without limitation the rights to use, copy, modify, merge, publish, */
|
||||
/* distribute, sublicense, and/or sell copies of the Software, and to */
|
||||
/* permit persons to whom the Software is furnished to do so, subject to */
|
||||
/* the following conditions: */
|
||||
/* */
|
||||
/* The above copyright notice and this permission notice shall be */
|
||||
/* included in all copies or substantial portions of the Software. */
|
||||
/* */
|
||||
/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, */
|
||||
/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF */
|
||||
/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
|
||||
/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY */
|
||||
/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, */
|
||||
/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE */
|
||||
/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */
|
||||
/*************************************************************************/
|
||||
|
||||
#include "transform_2d.h"
|
||||
|
||||
void Transform2D::invert() {
|
||||
// FIXME: this function assumes the basis is a rotation matrix, with no scaling.
|
||||
// Transform2D::affine_inverse can handle matrices with scaling, so GDScript should eventually use that.
|
||||
SWAP(elements[0][1], elements[1][0]);
|
||||
elements[2] = basis_xform(-elements[2]);
|
||||
}
|
||||
|
||||
Transform2D Transform2D::inverse() const {
|
||||
|
||||
Transform2D inv = *this;
|
||||
inv.invert();
|
||||
return inv;
|
||||
}
|
||||
|
||||
void Transform2D::affine_invert() {
|
||||
|
||||
real_t det = basis_determinant();
|
||||
#ifdef MATH_CHECKS
|
||||
ERR_FAIL_COND(det == 0);
|
||||
#endif
|
||||
real_t idet = 1.0 / det;
|
||||
|
||||
SWAP(elements[0][0], elements[1][1]);
|
||||
elements[0] *= Vector2(idet, -idet);
|
||||
elements[1] *= Vector2(-idet, idet);
|
||||
|
||||
elements[2] = basis_xform(-elements[2]);
|
||||
}
|
||||
|
||||
Transform2D Transform2D::affine_inverse() const {
|
||||
|
||||
Transform2D inv = *this;
|
||||
inv.affine_invert();
|
||||
return inv;
|
||||
}
|
||||
|
||||
void Transform2D::rotate(real_t p_phi) {
|
||||
*this = Transform2D(p_phi, Vector2()) * (*this);
|
||||
}
|
||||
|
||||
real_t Transform2D::get_rotation() const {
|
||||
real_t det = basis_determinant();
|
||||
Transform2D m = orthonormalized();
|
||||
if (det < 0) {
|
||||
m.scale_basis(Size2(1, -1)); // convention to separate rotation and reflection for 2D is to absorb a flip along y into scaling.
|
||||
}
|
||||
return Math::atan2(m[0].y, m[0].x);
|
||||
}
|
||||
|
||||
void Transform2D::set_rotation(real_t p_rot) {
|
||||
|
||||
real_t cr = Math::cos(p_rot);
|
||||
real_t sr = Math::sin(p_rot);
|
||||
elements[0][0] = cr;
|
||||
elements[0][1] = sr;
|
||||
elements[1][0] = -sr;
|
||||
elements[1][1] = cr;
|
||||
}
|
||||
|
||||
Transform2D::Transform2D(real_t p_rot, const Vector2 &p_pos) {
|
||||
|
||||
real_t cr = Math::cos(p_rot);
|
||||
real_t sr = Math::sin(p_rot);
|
||||
elements[0][0] = cr;
|
||||
elements[0][1] = sr;
|
||||
elements[1][0] = -sr;
|
||||
elements[1][1] = cr;
|
||||
elements[2] = p_pos;
|
||||
}
|
||||
|
||||
Size2 Transform2D::get_scale() const {
|
||||
real_t det_sign = basis_determinant() > 0 ? 1 : -1;
|
||||
return Size2(elements[0].length(), det_sign * elements[1].length());
|
||||
}
|
||||
|
||||
void Transform2D::scale(const Size2 &p_scale) {
|
||||
scale_basis(p_scale);
|
||||
elements[2] *= p_scale;
|
||||
}
|
||||
void Transform2D::scale_basis(const Size2 &p_scale) {
|
||||
|
||||
elements[0][0] *= p_scale.x;
|
||||
elements[0][1] *= p_scale.y;
|
||||
elements[1][0] *= p_scale.x;
|
||||
elements[1][1] *= p_scale.y;
|
||||
}
|
||||
void Transform2D::translate(real_t p_tx, real_t p_ty) {
|
||||
|
||||
translate(Vector2(p_tx, p_ty));
|
||||
}
|
||||
void Transform2D::translate(const Vector2 &p_translation) {
|
||||
|
||||
elements[2] += basis_xform(p_translation);
|
||||
}
|
||||
|
||||
void Transform2D::orthonormalize() {
|
||||
|
||||
// Gram-Schmidt Process
|
||||
|
||||
Vector2 x = elements[0];
|
||||
Vector2 y = elements[1];
|
||||
|
||||
x.normalize();
|
||||
y = (y - x * (x.dot(y)));
|
||||
y.normalize();
|
||||
|
||||
elements[0] = x;
|
||||
elements[1] = y;
|
||||
}
|
||||
Transform2D Transform2D::orthonormalized() const {
|
||||
|
||||
Transform2D on = *this;
|
||||
on.orthonormalize();
|
||||
return on;
|
||||
}
|
||||
|
||||
bool Transform2D::operator==(const Transform2D &p_transform) const {
|
||||
|
||||
for (int i = 0; i < 3; i++) {
|
||||
if (elements[i] != p_transform.elements[i])
|
||||
return false;
|
||||
}
|
||||
|
||||
return true;
|
||||
}
|
||||
|
||||
bool Transform2D::operator!=(const Transform2D &p_transform) const {
|
||||
|
||||
for (int i = 0; i < 3; i++) {
|
||||
if (elements[i] != p_transform.elements[i])
|
||||
return true;
|
||||
}
|
||||
|
||||
return false;
|
||||
}
|
||||
|
||||
void Transform2D::operator*=(const Transform2D &p_transform) {
|
||||
|
||||
elements[2] = xform(p_transform.elements[2]);
|
||||
|
||||
real_t x0, x1, y0, y1;
|
||||
|
||||
x0 = tdotx(p_transform.elements[0]);
|
||||
x1 = tdoty(p_transform.elements[0]);
|
||||
y0 = tdotx(p_transform.elements[1]);
|
||||
y1 = tdoty(p_transform.elements[1]);
|
||||
|
||||
elements[0][0] = x0;
|
||||
elements[0][1] = x1;
|
||||
elements[1][0] = y0;
|
||||
elements[1][1] = y1;
|
||||
}
|
||||
|
||||
Transform2D Transform2D::operator*(const Transform2D &p_transform) const {
|
||||
|
||||
Transform2D t = *this;
|
||||
t *= p_transform;
|
||||
return t;
|
||||
}
|
||||
|
||||
Transform2D Transform2D::scaled(const Size2 &p_scale) const {
|
||||
|
||||
Transform2D copy = *this;
|
||||
copy.scale(p_scale);
|
||||
return copy;
|
||||
}
|
||||
|
||||
Transform2D Transform2D::basis_scaled(const Size2 &p_scale) const {
|
||||
|
||||
Transform2D copy = *this;
|
||||
copy.scale_basis(p_scale);
|
||||
return copy;
|
||||
}
|
||||
|
||||
Transform2D Transform2D::untranslated() const {
|
||||
|
||||
Transform2D copy = *this;
|
||||
copy.elements[2] = Vector2();
|
||||
return copy;
|
||||
}
|
||||
|
||||
Transform2D Transform2D::translated(const Vector2 &p_offset) const {
|
||||
|
||||
Transform2D copy = *this;
|
||||
copy.translate(p_offset);
|
||||
return copy;
|
||||
}
|
||||
|
||||
Transform2D Transform2D::rotated(real_t p_phi) const {
|
||||
|
||||
Transform2D copy = *this;
|
||||
copy.rotate(p_phi);
|
||||
return copy;
|
||||
}
|
||||
|
||||
real_t Transform2D::basis_determinant() const {
|
||||
|
||||
return elements[0].x * elements[1].y - elements[0].y * elements[1].x;
|
||||
}
|
||||
|
||||
Transform2D Transform2D::interpolate_with(const Transform2D &p_transform, real_t p_c) const {
|
||||
|
||||
//extract parameters
|
||||
Vector2 p1 = get_origin();
|
||||
Vector2 p2 = p_transform.get_origin();
|
||||
|
||||
real_t r1 = get_rotation();
|
||||
real_t r2 = p_transform.get_rotation();
|
||||
|
||||
Size2 s1 = get_scale();
|
||||
Size2 s2 = p_transform.get_scale();
|
||||
|
||||
//slerp rotation
|
||||
Vector2 v1(Math::cos(r1), Math::sin(r1));
|
||||
Vector2 v2(Math::cos(r2), Math::sin(r2));
|
||||
|
||||
real_t dot = v1.dot(v2);
|
||||
|
||||
dot = (dot < -1.0) ? -1.0 : ((dot > 1.0) ? 1.0 : dot); //clamp dot to [-1,1]
|
||||
|
||||
Vector2 v;
|
||||
|
||||
if (dot > 0.9995) {
|
||||
v = Vector2::linear_interpolate(v1, v2, p_c).normalized(); //linearly interpolate to avoid numerical precision issues
|
||||
} else {
|
||||
real_t angle = p_c * Math::acos(dot);
|
||||
Vector2 v3 = (v2 - v1 * dot).normalized();
|
||||
v = v1 * Math::cos(angle) + v3 * Math::sin(angle);
|
||||
}
|
||||
|
||||
//construct matrix
|
||||
Transform2D res(Math::atan2(v.y, v.x), Vector2::linear_interpolate(p1, p2, p_c));
|
||||
res.scale_basis(Vector2::linear_interpolate(s1, s2, p_c));
|
||||
return res;
|
||||
}
|
||||
|
||||
Transform2D::operator String() const {
|
||||
|
||||
return String(String() + elements[0] + ", " + elements[1] + ", " + elements[2]);
|
||||
}
|
||||
201
core/math/transform_2d.h
Normal file
201
core/math/transform_2d.h
Normal file
|
|
@ -0,0 +1,201 @@
|
|||
/*************************************************************************/
|
||||
/* transform_2d.h */
|
||||
/*************************************************************************/
|
||||
/* This file is part of: */
|
||||
/* GODOT ENGINE */
|
||||
/* https://godotengine.org */
|
||||
/*************************************************************************/
|
||||
/* Copyright (c) 2007-2018 Juan Linietsky, Ariel Manzur. */
|
||||
/* Copyright (c) 2014-2018 Godot Engine contributors (cf. AUTHORS.md) */
|
||||
/* */
|
||||
/* Permission is hereby granted, free of charge, to any person obtaining */
|
||||
/* a copy of this software and associated documentation files (the */
|
||||
/* "Software"), to deal in the Software without restriction, including */
|
||||
/* without limitation the rights to use, copy, modify, merge, publish, */
|
||||
/* distribute, sublicense, and/or sell copies of the Software, and to */
|
||||
/* permit persons to whom the Software is furnished to do so, subject to */
|
||||
/* the following conditions: */
|
||||
/* */
|
||||
/* The above copyright notice and this permission notice shall be */
|
||||
/* included in all copies or substantial portions of the Software. */
|
||||
/* */
|
||||
/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, */
|
||||
/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF */
|
||||
/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
|
||||
/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY */
|
||||
/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, */
|
||||
/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE */
|
||||
/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */
|
||||
/*************************************************************************/
|
||||
|
||||
#ifndef TRANSFORM_2D_H
|
||||
#define TRANSFORM_2D_H
|
||||
|
||||
#include "rect2.h" // also includes vector2, math_funcs, and ustring
|
||||
|
||||
struct Transform2D {
|
||||
// Warning #1: basis of Transform2D is stored differently from Basis. In terms of elements array, the basis matrix looks like "on paper":
|
||||
// M = (elements[0][0] elements[1][0])
|
||||
// (elements[0][1] elements[1][1])
|
||||
// This is such that the columns, which can be interpreted as basis vectors of the coordinate system "painted" on the object, can be accessed as elements[i].
|
||||
// Note that this is the opposite of the indices in mathematical texts, meaning: $M_{12}$ in a math book corresponds to elements[1][0] here.
|
||||
// This requires additional care when working with explicit indices.
|
||||
// See https://en.wikipedia.org/wiki/Row-_and_column-major_order for further reading.
|
||||
|
||||
// Warning #2: 2D be aware that unlike 3D code, 2D code uses a left-handed coordinate system: Y-axis points down,
|
||||
// and angle is measure from +X to +Y in a clockwise-fashion.
|
||||
|
||||
Vector2 elements[3];
|
||||
|
||||
_FORCE_INLINE_ real_t tdotx(const Vector2 &v) const { return elements[0][0] * v.x + elements[1][0] * v.y; }
|
||||
_FORCE_INLINE_ real_t tdoty(const Vector2 &v) const { return elements[0][1] * v.x + elements[1][1] * v.y; }
|
||||
|
||||
const Vector2 &operator[](int p_idx) const { return elements[p_idx]; }
|
||||
Vector2 &operator[](int p_idx) { return elements[p_idx]; }
|
||||
|
||||
_FORCE_INLINE_ Vector2 get_axis(int p_axis) const {
|
||||
ERR_FAIL_INDEX_V(p_axis, 3, Vector2());
|
||||
return elements[p_axis];
|
||||
}
|
||||
_FORCE_INLINE_ void set_axis(int p_axis, const Vector2 &p_vec) {
|
||||
ERR_FAIL_INDEX(p_axis, 3);
|
||||
elements[p_axis] = p_vec;
|
||||
}
|
||||
|
||||
void invert();
|
||||
Transform2D inverse() const;
|
||||
|
||||
void affine_invert();
|
||||
Transform2D affine_inverse() const;
|
||||
|
||||
void set_rotation(real_t p_rot);
|
||||
real_t get_rotation() const;
|
||||
_FORCE_INLINE_ void set_rotation_and_scale(real_t p_rot, const Size2 &p_scale);
|
||||
void rotate(real_t p_phi);
|
||||
|
||||
void scale(const Size2 &p_scale);
|
||||
void scale_basis(const Size2 &p_scale);
|
||||
void translate(real_t p_tx, real_t p_ty);
|
||||
void translate(const Vector2 &p_translation);
|
||||
|
||||
real_t basis_determinant() const;
|
||||
|
||||
Size2 get_scale() const;
|
||||
|
||||
_FORCE_INLINE_ const Vector2 &get_origin() const { return elements[2]; }
|
||||
_FORCE_INLINE_ void set_origin(const Vector2 &p_origin) { elements[2] = p_origin; }
|
||||
|
||||
Transform2D scaled(const Size2 &p_scale) const;
|
||||
Transform2D basis_scaled(const Size2 &p_scale) const;
|
||||
Transform2D translated(const Vector2 &p_offset) const;
|
||||
Transform2D rotated(real_t p_phi) const;
|
||||
|
||||
Transform2D untranslated() const;
|
||||
|
||||
void orthonormalize();
|
||||
Transform2D orthonormalized() const;
|
||||
|
||||
bool operator==(const Transform2D &p_transform) const;
|
||||
bool operator!=(const Transform2D &p_transform) const;
|
||||
|
||||
void operator*=(const Transform2D &p_transform);
|
||||
Transform2D operator*(const Transform2D &p_transform) const;
|
||||
|
||||
Transform2D interpolate_with(const Transform2D &p_transform, real_t p_c) const;
|
||||
|
||||
_FORCE_INLINE_ Vector2 basis_xform(const Vector2 &p_vec) const;
|
||||
_FORCE_INLINE_ Vector2 basis_xform_inv(const Vector2 &p_vec) const;
|
||||
_FORCE_INLINE_ Vector2 xform(const Vector2 &p_vec) const;
|
||||
_FORCE_INLINE_ Vector2 xform_inv(const Vector2 &p_vec) const;
|
||||
_FORCE_INLINE_ Rect2 xform(const Rect2 &p_rect) const;
|
||||
_FORCE_INLINE_ Rect2 xform_inv(const Rect2 &p_rect) const;
|
||||
|
||||
operator String() const;
|
||||
|
||||
Transform2D(real_t xx, real_t xy, real_t yx, real_t yy, real_t ox, real_t oy) {
|
||||
|
||||
elements[0][0] = xx;
|
||||
elements[0][1] = xy;
|
||||
elements[1][0] = yx;
|
||||
elements[1][1] = yy;
|
||||
elements[2][0] = ox;
|
||||
elements[2][1] = oy;
|
||||
}
|
||||
|
||||
Transform2D(real_t p_rot, const Vector2 &p_pos);
|
||||
Transform2D() {
|
||||
elements[0][0] = 1.0;
|
||||
elements[1][1] = 1.0;
|
||||
}
|
||||
};
|
||||
|
||||
Vector2 Transform2D::basis_xform(const Vector2 &p_vec) const {
|
||||
|
||||
return Vector2(
|
||||
tdotx(p_vec),
|
||||
tdoty(p_vec));
|
||||
}
|
||||
|
||||
Vector2 Transform2D::basis_xform_inv(const Vector2 &p_vec) const {
|
||||
|
||||
return Vector2(
|
||||
elements[0].dot(p_vec),
|
||||
elements[1].dot(p_vec));
|
||||
}
|
||||
|
||||
Vector2 Transform2D::xform(const Vector2 &p_vec) const {
|
||||
|
||||
return Vector2(
|
||||
tdotx(p_vec),
|
||||
tdoty(p_vec)) +
|
||||
elements[2];
|
||||
}
|
||||
Vector2 Transform2D::xform_inv(const Vector2 &p_vec) const {
|
||||
|
||||
Vector2 v = p_vec - elements[2];
|
||||
|
||||
return Vector2(
|
||||
elements[0].dot(v),
|
||||
elements[1].dot(v));
|
||||
}
|
||||
Rect2 Transform2D::xform(const Rect2 &p_rect) const {
|
||||
|
||||
Vector2 x = elements[0] * p_rect.size.x;
|
||||
Vector2 y = elements[1] * p_rect.size.y;
|
||||
Vector2 pos = xform(p_rect.position);
|
||||
|
||||
Rect2 new_rect;
|
||||
new_rect.position = pos;
|
||||
new_rect.expand_to(pos + x);
|
||||
new_rect.expand_to(pos + y);
|
||||
new_rect.expand_to(pos + x + y);
|
||||
return new_rect;
|
||||
}
|
||||
|
||||
void Transform2D::set_rotation_and_scale(real_t p_rot, const Size2 &p_scale) {
|
||||
|
||||
elements[0][0] = Math::cos(p_rot) * p_scale.x;
|
||||
elements[1][1] = Math::cos(p_rot) * p_scale.y;
|
||||
elements[1][0] = -Math::sin(p_rot) * p_scale.y;
|
||||
elements[0][1] = Math::sin(p_rot) * p_scale.x;
|
||||
}
|
||||
|
||||
Rect2 Transform2D::xform_inv(const Rect2 &p_rect) const {
|
||||
|
||||
Vector2 ends[4] = {
|
||||
xform_inv(p_rect.position),
|
||||
xform_inv(Vector2(p_rect.position.x, p_rect.position.y + p_rect.size.y)),
|
||||
xform_inv(Vector2(p_rect.position.x + p_rect.size.x, p_rect.position.y + p_rect.size.y)),
|
||||
xform_inv(Vector2(p_rect.position.x + p_rect.size.x, p_rect.position.y))
|
||||
};
|
||||
|
||||
Rect2 new_rect;
|
||||
new_rect.position = ends[0];
|
||||
new_rect.expand_to(ends[1]);
|
||||
new_rect.expand_to(ends[2]);
|
||||
new_rect.expand_to(ends[3]);
|
||||
|
||||
return new_rect;
|
||||
}
|
||||
|
||||
#endif // TRANSFORM_2D_H
|
||||
Loading…
Reference in New Issue
Block a user