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Updated tutorial_vector_math (markdown)

reduz 2014-11-16 05:52:52 -08:00
parent 400c87f647
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tutorial_vector_math.md

@ -453,15 +453,30 @@ Also, the resulting cross product of two normal vectors is _not_ a normal vector
### Area of a Triangle
Cross product can be used to obtain the surface area of a triangle in 3D. Given a triangle consisting of 3 points, A, B C, the area of the triangle is:
Cross product can be used to obtain the surface area of a triangle in 3D. Given a triangle consisting of 3 points, A, B C:
```python
var area = (A-B).cross(A-C).length()
<p align="center"><img src="images/tutovec17.png"></p>
Take any of them as a pivot and compute the adjacent vectors to the other two points. As example, we will use B as a pivot:
```
var BA = A-B
var BC = C-B
```
Which means, given the adjacent vectors of any of the points, the length of the resulting perpendicular vector is the triangle surface.
<p align="center"><img src="images/tutovec18.png"></p>
However, something else can be done with that perpendicular vector. If normalized, that vector becomes the normal of the triangle, so..
The surface area is computed by doing the cross product between the adjacent vectors:
```python
var area = BA.cross(BC).length()
```
However, something else can be done with that perpendicular vector.
<p align="center"><img src="images/tutovec19.png"></p>
If normalized, that vector becomes the normal of the triangle, so..
### Plane from a Triangle
@ -470,4 +485,3 @@ By using the same method to obtain the area but normalizing the resulting vector