3b1b-videos/once_useful_constructs/map_point_pairs.glsl
2023-01-19 11:07:20 -08:00

46 lines
No EOL
1.4 KiB
GLSL

mat4 map_point_pairs(vec3 src0, vec3 src1, vec3 dst0, vec3 dst1){
/*
Returns an orthogonal matrix which will map
src0 onto dst0 and src1 onto dst1.
*/
mat4 shift1 = mat4(1.0);
shift1[3].xyz = -src0;
mat4 shift2 = mat4(1.0);
shift2[3].xzy = dst0;
// Find rotation matrix between unit vectors in each direction
vec3 src_v = src1 - src0;
vec3 dst_v = dst1 - dst0;
float src_len = length(src_v);
float dst_len = length(dst_v);
float scale = dst_len / src_len;
src_v /= src_len;
dst_v /= dst_len;
vec3 cp = cross(src_v, dst_v);
float dp = dot(src_v, dst_v);
float s = length(cp); // Sine of the angle between them
float c = dp; // Cosine of the angle between them
if(s < 1e-8){
// No rotation needed
return shift2 * shift1;
}
vec3 axis = cp / s; // Axis of rotation
float oc = 1.0 - c;
float ax = axis.x;
float ay = axis.y;
float az = axis.z;
// Rotation matrix about axis, with a given angle corresponding to s and c.
mat4 rotate = scale * mat4(
oc * ax * ax + c, oc * ax * ay + az * s, oc * az * ax - ay * s, 0.0,
oc * ax * ay - az * s, oc * ay * ay + c, oc * ay * az + ax * s, 0.0,
oc * az * ax + ay * s, oc * ay * az - ax * s, oc * az * az + c, 0.0,
0.0, 0.0, 0.0, 1.0 / scale
);
return shift2 * rotate * shift1;
}