Game Development Reference
In-Depth Information
q13 = a*c;
q14 = a*d;
q22 = b*b;
q23 = b*c;
q24 = b*d;
q33 = c*c;
q34 = c*d;
q44 = d*d;
v.x = 0.0; v.y = 0.0; v.z = 0.0;
valid = TRUE;
deleted = FALSE;
}
The function that is used in the ReducePolygons function to create plane
quadrics is the member function CreateFromPoints . This function will
create the quadric directly from any three points in the plane. The algebra
was shown earlier in the chapter. By passing the three points in the
triangular polygon we can construct a plane quadric. Summing these
plane quadrics for the polygons meeting at a vertex gives the vertex
quadric. Since we are interested in vertex quadrics, we must build these
from plane quadrics. The speed of the ReducePolygons function could be
improved by creating an array of plane quadrics so that the fundamental
quadric is calculated only once.
BOOL CQuadric::CreateFromPoints(POINT3D &p1, POINT3D &p2, POINT3D
&p3)
{
double a, b, c, d, k,m, n,s, v, w;
k = p2.x/p3.x;
m = p1.x/p2.x;
n = (p1.y - m*p2.y)/(p2.y - k*p3.y);
s = (p1.z - m*p2.z - n*(p2.z - k*p3.z))/(n + k*n - 1 +m);
v = (s*(m - 1) - p1.z + m*p2.z)/(p1.y - m*p2.y);
w = (v*p1.y + p1.z +s)/p1.x;
c = sqrt(1.0/(1 + w*w + v*v));
a = -c*w;
b = c*v;
d = c*s;
q11 = a*a;
q12 = a*b;
q13 = a*c;
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