Fundamental Shader Concepts - Graphics Shaders - page 52

// the Bezier basis functions and their derivatives:
float bu0 = (1.-u) * (1.-u) * (1.-u);
float bu1 = 3. * u * (1.-u) * (1.-u);
float bu2 = 3. * u * u * (1.-u);
float bu3 = u * u * u;
float dbu0 = -3. * (1.-u) * (1.-u);
float dbu1 = 3. * (1.-u) * (1.-3.*u);
float dbu2 = 3. * u * (2.-3.*u);
float dbu3 = 3. * u * u;
float bv0 = (1.-v) * (1.-v) * (1.-v);
float bv1 = 3. * v * (1.-v) * (1.-v);
float bv2 = 3. * v * v * (1.-v);
float bv3 = v * v * v;
float dbv0 = -3. * (1.-v) * (1.-v);
float dbv1 = 3. * (1.-v) * (1.-3.*v);
float dbv2 = 3. * v * (2.-3.*v);
float dbv3 = 3. * v * v;
// finally we get to compute something
gl_Position = bu0 * ( bv0*p00 + bv1*p01 + bv2*p02 + bv3*p03 )
+ bu1 * ( bv0*p10 + bv1*p11 + bv2*p12 + bv3*p13 )
+ bu2 * ( bv0*p20 + bv1*p21 + bv2*p22 + bv3*p23 )
+ bu3 * ( bv0*p30 + bv1*p31 + bv2*p32 + bv3*p33 );
vec4 dpdu = dbu0 * ( bv0*p00 + bv1*p01 + bv2*p02 + bv3*p03 )
+ dbu1 * ( bv0*p10 + bv1*p11 + bv2*p12 + bv3*p13 )
+ dbu2 * ( bv0*p20 + bv1*p21 + bv2*p22 + bv3*p23 )
+ dbu3 * ( bv0*p30 + bv1*p31 + bv2*p32 + bv3*p33 );
vec4 dpdv = bu0 * ( dbv0*p00 + dbv1*p01 + dbv2*p02 +
dbv3*p03 )
+ bu1 * ( dbv0*p10 + dbv1*p11 + dbv2*p12 +
dbv3*p13 )
+ bu2 * ( dbv0*p20 + dbv1*p21 + dbv2*p22 +
dbv3*p23 )
+ bu3 * ( dbv0*p30 + dbv1*p31 + dbv2*p32 +
dbv3*p33 );
teNormal = normalize( cross( dpdu.xyz, dpdv.xyz ) );
}