This commit is contained in:
Grant Sanderson 2023-01-17 17:39:32 -08:00
parent b7831ef3f1
commit 9ed8dd5439
2 changed files with 29 additions and 38 deletions

View file

@ -47,10 +47,10 @@ vec2 xs_on_clean_parabola(vec3 b0, vec3 b1, vec3 b2){
}
mat3 map_point_pairs(vec2 src0, vec2 src1, vec2 dest0, vec2 dest1){
mat3 map_point_pairs(vec2 src0, vec2 src1, vec2 dst0, vec2 dst1){
/*
Returns an orthogonal matrix which will map
src0 onto dest0 and src1 onto dest1.
src0 onto dst0 and src1 onto dst1.
*/
mat3 shift1 = mat3(
1.0, 0.0, 0.0,
@ -60,11 +60,11 @@ mat3 map_point_pairs(vec2 src0, vec2 src1, vec2 dest0, vec2 dest1){
mat3 shift2 = mat3(
1.0, 0.0, 0.0,
0.0, 1.0, 0.0,
dest0.x, dest0.y, 1.0
dst0.x, dst0.y, 1.0
);
// Compute complex division dest_vect / src_vect to determine rotation
vec2 complex_rot = complex_div(dest1 - dest0, src1 - src0);
vec2 complex_rot = complex_div(dst1 - dst0, src1 - src0);
mat3 rotate = mat3(
complex_rot.x, complex_rot.y, 0.0,
-complex_rot.y, complex_rot.x, 0.0,
@ -96,27 +96,19 @@ mat4 map_triangles(vec3 src0, vec3 src1, vec3 src2, vec3 dst0, vec3 dst1, vec3 d
}
mat4 map_point_pairs(vec3 src0, vec3 src1, vec3 dest0, vec3 dest1){
mat4 map_point_pairs(vec3 src0, vec3 src1, vec3 dst0, vec3 dst1){
/*
Returns an orthogonal matrix which will map
src0 onto dest0 and src1 onto dest1.
src0 onto dst0 and src1 onto dst1.
*/
mat4 shift1 = mat4(
1.0, 0.0, 0.0, 0.0,
0.0, 1.0, 0.0, 0.0,
0.0, 0.0, 1.0, 0.0,
-src0.x, -src0.y, -src0.z, 1.0
);
mat4 shift2 = mat4(
1.0, 0.0, 0.0, 0.0,
0.0, 1.0, 0.0, 0.0,
0.0, 0.0, 1.0, 0.0,
dest0.x, dest0.y, dest0.z, 1.0
);
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 = dest1 - dest0;
vec3 dst_v = dst1 - dst0;
float src_len = length(src_v);
float dst_len = length(dst_v);
float scale = dst_len / src_len;
@ -158,9 +150,9 @@ 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 dest0;
vec3 dest1;
vec3 dest2;
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.
@ -172,20 +164,20 @@ 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{
dest0 = vec3(x0, x0 * x0, 0.0);
dest1 = vec3(0.5 * (x0 + x2), x0 * x2, 0.0);
dest2 = vec3(x2, x2 * x2, 0.0);
dst0 = vec3(x0, x0 * x0, 0.0);
dst1 = vec3(0.5 * (x0 + x2), x0 * x2, 0.0);
dst2 = vec3(x2, x2 * x2, 0.0);
}
}
// Check if is_linear status changed above
if (bool(is_linear)){
dest0 = vec3(0.0, 0.0, 0.0);
dest2 = vec3(1.0, 0.0, 0.0);
return map_point_pairs(b0, b2, dest0, dest2);
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, dest0, dest1);
return map_triangles(b0, b1, b2, dest0, dest1, dest2);
// return map_point_pairs(b0, b2, dst0, dst1);
return map_triangles(b0, b1, b2, dst0, dst1, dst2);
}
@ -195,8 +187,8 @@ mat3 get_xy_to_uv(vec2 b0, vec2 b1, vec2 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.
*/
vec2 dest0;
vec2 dest1;
vec2 dst0;
vec2 dst1;
is_linear = temp_is_linear;
// Portions of the parabola y = x^2 where abs(x) exceeds
// this value are treated as straight lines.
@ -208,15 +200,15 @@ mat3 get_xy_to_uv(vec2 b0, vec2 b1, vec2 b2, float temp_is_linear, out float is_
if((x0 > thresh && x2 > thresh) || (x0 < -thresh && x2 < -thresh)){
is_linear = 1.0;
}else{
dest0 = vec2(x0, x0 * x0);
dest1 = vec2(x2, x2 * x2);
dst0 = vec2(x0, x0 * x0);
dst1 = vec2(x2, x2 * x2);
}
}
// Check if is_linear status changed above
if (bool(is_linear)){
dest0 = vec2(0, 0);
dest1 = vec2(1, 0);
dst0 = vec2(0, 0);
dst1 = vec2(1, 0);
}
return map_point_pairs(b0, b2, dest0, dest1);
return map_point_pairs(b0, b2, dst0, dst1);
}

View file

@ -178,7 +178,6 @@ void main() {
// coincides with y = x^2, between some values x0 and x2. Or, in
// the case of a linear curve (bezier degree 1), just put it on
// the segment from (0, 0) to (1, 0)
// mat3 xy_to_uv = get_xy_to_uv(p0.xy, p1.xy, p2.xy, is_linear, is_linear);
mat4 xyz_to_uv = get_xyz_to_uv(p0, p1, p2, is_linear, is_linear);
float uv_scale_factor = length(xyz_to_uv[0].xyz);