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uint findMSB(uint x)
{
uint i;
uint mask;
uint res = -1;
for (i = 0; i < 32; i++)
{
mask = 0x80000000 >> i;
if ((x & mask) != 0)
{
res = 31 - i;
break;
}
}
return res;
}
uint parentKey(in uint key)
{
return (key >> 1u);
}
void childrenKeys(in uint key, out uint children[2])
{
children[0] = (key << 1u) | 0u;
children[1] = (key << 1u) | 1u;
}
bool isRootKey(in uint key)
{
return (key == 1u);
}
bool isLeafKey(in uint key)
{
return findMSB(key) == 31;
}
bool isChildZeroKey(in uint key)
{
return ((key & 1u) == 0u);
}
// barycentric interpolation
vec3 berp(in vec3 v[3], in vec2 u)
{
return v[0] + u.x * (v[1] - v[0]) + u.y * (v[2] - v[0]);
}
vec4 berp(in vec4 v[3], in vec2 u)
{
return v[0] + u.x * (v[1] - v[0]) + u.y * (v[2] - v[0]);
}
// get xform from bit value
mat3 bitToXform(in uint bit)
{
float b = float(bit);
float c = 1.0f - b;
vec3 c1 = vec3(0.0f, c , b );
vec3 c2 = vec3(0.5f, b , 0.0f);
vec3 c3 = vec3(0.5f, 0.0f, c );
return mtxFromCols(c1, c2, c3);
}
// get xform from key
mat3 keyToXform(in uint key)
{
vec3 c1 = vec3(1.0f, 0.0f, 0.0f);
vec3 c2 = vec3(0.0f, 1.0f, 0.0f);
vec3 c3 = vec3(0.0f, 0.0f, 1.0f);
mat3 xf = mtxFromCols(c1, c2, c3);
while (key > 1u) {
xf = mul(xf, bitToXform(key & 1u));
key = key >> 1u;
}
return xf;
}
// get xform from key as well as xform from parent key
mat3 keyToXform(in uint key, out mat3 xfp)
{
xfp = keyToXform(parentKey(key));
return keyToXform(key);
}
// subdivision routine (vertex position only)
void subd(in uint key, in vec4 v_in[3], out vec4 v_out[3])
{
mat3 xf = keyToXform(key);
mat4x3 m = mtxFromRows(v_in[0], v_in[1], v_in[2]);
mat4x3 v = mul(xf, m);
v_out[0] = mtxGetRow(v, 0);
v_out[1] = mtxGetRow(v, 1);
v_out[2] = mtxGetRow(v, 2);
}
// subdivision routine (vertex position only)
// also computes parent position
void subd(in uint key, in vec4 v_in[3], out vec4 v_out[3], out vec4 v_out_p[3])
{
mat3 xfp; mat3 xf = keyToXform(key, xfp);
mat4x3 m = mtxFromRows(v_in[0], v_in[1], v_in[2]);
mat4x3 v = mul(xf, m);
mat4x3 vp = mul(xfp, m);
v_out[0] = mtxGetRow(v, 0);
v_out[1] = mtxGetRow(v, 1);
v_out[2] = mtxGetRow(v, 2);
v_out_p[0] = mtxGetRow(vp, 0);
v_out_p[1] = mtxGetRow(vp, 1);
v_out_p[2] = mtxGetRow(vp, 2);
}
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