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Simpler xyz-to-uv map for linear case

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This commit is contained in:
Grant Sanderson 2023-01-18 10:57:14 -08:00
parent 874906bedf
commit 1a663943c9
1 changed files with 23 additions and 44 deletions
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67
manimlib/shaders/inserts/get_xy_to_uv.glsl
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@ -39,51 +39,36 @@ mat4 map_triangles(vec3 src0, vec3 src1, vec3 src2, vec3 dst0, vec3 dst1, vec3 d
}
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;
mat4 map_onto_x_axis(vec3 src0, vec3 src1){
mat4 shift = mat4(1.0);
shift[3].xyz = -src0;
// 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 vect = normalize(src1 - src0);
// This is the same as cross(vect, vec3(1, 0, 0))
vec3 axis = vec3(0.0, vect.z, -vect.y);
vec3 cp = cross(src_v, dst_v);
float dp = dot(src_v, dst_v);
float s = length(axis); // Sine of the angle between them
float c = vect.x; // Cosine of the angle between them
float s = length(cp); // Sine of the angle between them
float c = dp; // Cosine of the angle between them
// No rotation needed
if(s < 1e-8) return shift;
if(s < 1e-8){
// No rotation needed
return shift2 * shift1;
}
vec3 axis = cp / s; // Axis of rotation
axis = axis / 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(
mat4 rotate = 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
0.0, 0.0, 0.0, 1.0
);
return shift2 * rotate * shift1;
return rotate * shift;
}
@ -93,9 +78,6 @@ mat4 get_xyz_to_uv(vec3 b0, vec3 b1, vec3 b2, float temp_is_linear, out float is
bezier controls points into a new coordinate system such that the bezier curve
coincides with y = x^2, or in the case of a linear curve, it's mapped to the x-axis.
*/
vec3 dst0;
vec3 dst1;
vec3 dst2;
is_linear = temp_is_linear;
// Portions of the parabola y = x^2 where abs(x) exceeds
// this value are treated as straight lines.
@ -107,18 +89,15 @@ mat4 get_xyz_to_uv(vec3 b0, vec3 b1, vec3 b2, float temp_is_linear, out float is
if((x0 > thresh && x2 > thresh) || (x0 < -thresh && x2 < -thresh)){
is_linear = 1.0;
}else{
dst0 = vec3(x0, x0 * x0, 0.0);
dst1 = vec3(0.5 * (x0 + x2), x0 * x2, 0.0);
dst2 = vec3(x2, x2 * x2, 0.0);
// This triangle on the xy plane should be isometric
// to (b0, b1, b2), and it should define a quadratic
// bezier segment aligned with y = x^2
vec3 dst0 = vec3(x0, x0 * x0, 0.0);
vec3 dst1 = vec3(0.5 * (x0 + x2), x0 * x2, 0.0);
vec3 dst2 = vec3(x2, x2 * x2, 0.0);
return map_triangles(b0, b1, b2, dst0, dst1, dst2);
}
}
// Check if is_linear status changed above
if (bool(is_linear)){
dst0 = vec3(0.0, 0.0, 0.0);
dst2 = vec3(1.0, 0.0, 0.0);
return map_point_pairs(b0, b2, dst0, dst2);
}
// return map_point_pairs(b0, b2, dst0, dst1);
return map_triangles(b0, b1, b2, dst0, dst1, dst2);
// Only lands here if is_linear is 1.0
return map_onto_x_axis(b0, b2);
}