1.9 KiB
| layout | title |
|---|---|
| math | Environment |
Affine Transforms & Vector Math
class Transformable {
// attaributes
PVector _position;
float _rotation;
float _scale;
...
public void display() {
pushMatrix();
translate(_position.x, _position.y);
rotate(_rotation);
scale(_scale);
draw_shape();
popMatrix();
}
...
};
What is a geometry / shape?
What types of (2D / 3D) transformations can we apply to geometries / shapes?
What is a matrix Matrix?
$ a, b, c], [d, e, f], [g, h, i $
Matrix [3 x 3] multiplication with a Vector [1 x 3]
$ a, b, c], [d, e, f], [g, h, i x], [y], [z = ax + by + cz], [dx + ey + fz], [gx + hy + iz $
What types of geometrical transformations (vertices transformation) can we perform using a Matrix?
Translation
$ 1, 0, tx], [0, 1, ty], [0, 0, 1 x], [y], [1 = dot x], [dot y], [1 $
Scaling
$ sx, 0, 0], [0, sy, 0], [0, 0, 1 x], [y], [1 = dot x], [dot y], [1 $
Rotation theta
$ cos theta, -sin theta, 0], [sin theta, cos theta, 0], [0, 0, 1 x], [y], [1 = dot x], [dot y], [1 $
Shearing
$ 1, shx, 0], [shy, 1, 0], [0, 0, 1 x], [y], [1 = dot x], [dot y], [1 $
What is an Affine Transform?
Affine Transform Matrix comprises a Translation, Scaling, Rotation and Shearing
$ sx * cos theta, -sin theta * shx, tx], [sin theta * shy, sy * cos theta, ty], [0, 0, 1 x], [y], [1 = dot x], [dot y], [1 $
Yes, but what other types of transformations exists?
