Affine

CGP provide also a set of helper structure to handle the combination of rotation, translation and scaling. Each transformation type is store and can be set individually, while the general structures can be combined together and apply to vectors as if it was a matrix.

Code Reference

- affine_rt.hpp
09_geometric_transformation/affine/affine_rt/affine_rt.hpp
- affine_rts.hpp
09_geometric_transformation/affine/affine_rts/affine_rts.hpp
- affine.hpp
09_geometric_transformation/affine/affine/affine.hpp

Structures

The structure affine_rt (for Rotation-Translation) and affine_rts (for Rotation-Translation-Scaling) are available to this effect and can be combined together.
struct affine_rt
rotation_transform rotation
vec3 translation
struct affine_rts
rotation_transform rotation
vec3 translation
float scaling
affine is a more general container that adds non-homogeneous scaling.
struct affine
rotation_transform rotation
vec3 translation
float scaling
vec3 scaling_xyz

Usage

affine_rts A;
A.rotation = rotation_transform::from_axis_angle({ 1,0,0 }, Pi / 4);
A.translation = { 1,1,2 };
A.scaling = 1.1f;

affine_rts B;
B.rotation = rotation_transform::from_axis_angle({ 0,1,0 }, Pi / 6);
B.translation = { 2,1,0 };
B.scaling = 2.0f;

// Combine the affine transforms using operator *
affine_rts C = A * B;

// The corresponding components of C can be obtained as
// C.rotation, C.translation, C.scaling

// Apply an affine transform to a vec3
vec3 p = C* vec3{ -3,2,0 };
//  assume that the vector is (-3,2,0,1) in homogeneous coordinates

// Retrieve the 4x4 matrix corresponding to the transform
mat4 T = C.matrix();
A possible use of affine_rt is to encode in a concise way a rotation with respect to a point (different from the origin). 
rotation_transform R; // Some rotation
vec3 c = { 1,2,3 }; // A position around which the rotation is applied

// Encode a "rotation around a given center"
affine_rt T = rotation_around_center(R, c);

// Apply the transformation to some coordinates
vec3 p = T * vec3{ 1.1f, 2.1f, 1.5f };