void* KB_PosInitialize(int numKeys, PositionKey* key)
{
assert(numKeys >= 4);
float omt0, omc0, opc0, omb0, opb0, adj0, out0, out1;
float omt1, omc1, opc1, omb1, opb1, adj1, in0, in1;
Point3 Tout, Tin;
Point3 DP;
SplineInfo* info = (SplineInfo*) calloc(1, sizeof(SplineInfo));
info->numPolys = numKeys-3;
info->poly = (CubicPolynomial*)
calloc(info->numPolys, sizeof(CubicPolynomial));
int i0 = 0, i1 = 1, i2 = 2, i3 = 3;
for (; i0 < info->numPolys; i0++, i1++, i2++, i3++)
{
/* Build P[i2] - P[i1]. */
DP.x = key[i2].P.x - key[i1].P.x;
DP.y = key[i2].P.y - key[i1].P.y;
DP.z = key[i2].P.z - key[i1].P.z;
/* Build multipliers at point P[i1]. Names are derived as follows:
* one - minus / plus - t / c / b */
omt0 = 1 - key[i1].tension; //1 - p1.t
omc0 = 1 - key[i1].continuity; //1 - p1.c
opc0 = 1 + key[i1].continuity; //1 + p1.c
omb0 = 1 - key[i1].bias; //1 - p1.b
opb0 = 1 + key[i1].bias; //1 + p1.b
/* I don't get this adjustment. It differs from the explanation on
Wikpedia, and the * 2 cancels with the / 2 later. */
adj0 = 2 * (key[i2].t - key[i1].t) / (key[i2].t - key[i0].t);
//2 * (t2 - t1) / (t2 - t0)
out0 = (adj0 * omt0 * opc0 * opb0) / 2;
out1 = (adj0 * omt0 * omc0 * omb0) / 2;
/* Build outgoing tangent at P[i1]. */
Tout.x = out1 * (DP.x) + out0 * (key[i1].P.x - key[i0].P.x);
Tout.y = out1 * (DP.y) + out0 * (key[i1].P.y - key[i0].P.y);
Tout.z = out1 * (DP.z) + out0 * (key[i1].P.z - key[i0].P.z);
/* Build multipliers at point P[i2]. */
omt1 = 1 - key[i2].tension; //1 - p2.t
omc1 = 1 - key[i2].continuity; //1 - p2.c
opc1 = 1 + key[i2].continuity; //1 + p2.c
omb1 = 1 - key[i2].bias; //1 - p2.b
opb1 = 1 + key[i2].bias; //1 + p2.b
adj1 = 2 * (key[i2].t - key[i1].t) / (key[i3].t - key[i1].t);
//2 * (t2 - t1) / (t3 - t1)
in0 = (adj1 * omt1 * omc1 * opb1) / 2;
in1 = (adj1 * omt1 * opc1 * omb1) / 2;
/* Build incoming tangent at P[i2]. */
Tin.x = in1 * (key[i3].P.x - key[i2].P.x) + in0 * (DP.x);
Tin.y = in1 * (key[i3].P.y - key[i2].P.y) + in0 * (DP.y);
Tin.z = in1 * (key[i3].P.z - key[i2].P.z) + in0 * (DP.z);
info->poly[i0].C0.x = key[i1].P.x;
info->poly[i0].C0.y = key[i1].P.y;
info->poly[i0].C0.z = key[i1].P.z;
info->poly[i0].C1.x = Tout.x;
info->poly[i0].C1.y = Tout.y;
info->poly[i0].C1.z = Tout.z;
info->poly[i0].C2.x = 3 * DP.x - 2 * Tout.x - Tin.x;
info->poly[i0].C2.y = 3 * DP.y - 2 * Tout.y - Tin.y;
info->poly[i0].C2.z = 3 * DP.z - 2 * Tout.z - Tin.z;
info->poly[i0].C3.x = -2 * DP.x + Tout.x + Tin.x;
info->poly[i0].C3.y = -2 * DP.y + Tout.y + Tin.y;
info->poly[i0].C3.z = -2 * DP.z + Tout.z + Tin.z;
info->poly[i0].tmin = key[i1].t;
info->poly[i0].tmax = key[i2].t;
info->poly[i0].trange = info->poly[i0].tmax - info->poly[i0].tmin;
}
ComputeArcLength(info);
return info;
}
/*-------------------------------------------------------------------------*/
void* KB_PosInitialize (int numKeys, PositionKey* key)
{
/* assert: numKeys >= 4 */
double omt0, omc0, opc0, omb0, opb0, adj0, out0, out1;
double omt1, omc1, opc1, omb1, opb1, adj1, in0, in1;
Point3 Tout, Tin;
Point3 DP;
int i0 = 0, i1 = 1, i2 = 2, i3 = 3;
SplineInfo* info = (SplineInfo*)calloc(1, sizeof(SplineInfo));
info->numPolys = numKeys-3;
info->poly = (CubicPolynomial*)calloc(info->numPolys, sizeof(CubicPolynomial));
for (/**/; i0 < info->numPolys; i0++, i1++, i2++, i3++)
{
/* build P[i2]-P[i1]; */
DP.x = key[i2].P.x - key[i1].P.x;
DP.y = key[i2].P.y - key[i1].P.y;
DP.z = key[i2].P.z - key[i1].P.z;
/* build multipliers at point P[i1] */
omt0 = 1-key[i1].tension;
omc0 = 1-key[i1].continuity;
opc0 = 1+key[i1].continuity;
omb0 = 1-key[i1].bias;
opb0 = 1+key[i1].bias;
adj0 = 2*(key[i2].t-key[i1].t)/(key[i2].t-key[i0].t);
out0 = 0.5*adj0*omt0*opc0*opb0;
out1 = 0.5*adj0*omt0*omc0*omb0;
/* build outgoing tangent at P[i1] */
Tout.x = out1*(DP.x)+out0*(key[i1].P.x-key[i0].P.x);
Tout.y = out1*(DP.y)+out0*(key[i1].P.y-key[i0].P.y);
Tout.z = out1*(DP.z)+out0*(key[i1].P.z-key[i0].P.z);
/* build multipliers at point P[i2] */
omt1 = 1-key[i2].tension;
omc1 = 1-key[i2].continuity;
opc1 = 1+key[i2].continuity;
omb1 = 1-key[i2].bias;
opb1 = 1+key[i2].bias;
adj1 = 2*(key[i2].t-key[i1].t)/(key[i3].t-key[i1].t);
in0 = 0.5*adj1*omt1*omc1*opb1;
in1 = 0.5*adj1*omt1*opc1*omb1;
/* build incoming tangent at P[i2] */
Tin.x = in1*(key[i3].P.x-key[i2].P.x)+in0*(DP.x);
Tin.y = in1*(key[i3].P.y-key[i2].P.y)+in0*(DP.y);
Tin.z = in1*(key[i3].P.z-key[i2].P.z)+in0*(DP.z);
info->poly[i0].C0.x = key[i1].P.x;
info->poly[i0].C0.y = key[i1].P.y;
info->poly[i0].C0.z = key[i1].P.z;
info->poly[i0].C1.x = Tout.x;
info->poly[i0].C1.y = Tout.y;
info->poly[i0].C1.z = Tout.z;
info->poly[i0].C2.x = 3*DP.x-2*Tout.x-Tin.x;
info->poly[i0].C2.y = 3*DP.y-2*Tout.y-Tin.y;
info->poly[i0].C2.z = 3*DP.z-2*Tout.z-Tin.z;
info->poly[i0].C3.x = -2*DP.x+Tout.x+Tin.x;
info->poly[i0].C3.y = -2*DP.y+Tout.y+Tin.y;
info->poly[i0].C3.z = -2*DP.z+Tout.z+Tin.z;
info->poly[i0].tmin = key[i1].t;
info->poly[i0].tmax = key[i2].t;
info->poly[i0].trange = info->poly[i0].tmax-info->poly[i0].tmin;
}
ComputeArcLength(info);
return info;
}
