bool ViewableTorus::FindIntersectionNT (
const VectorR3& viewPos, const VectorR3& viewDir,
double maxDistance, double *intersectDistance,
VisiblePoint& returnedPoint ) const
{
// Precheck for collisions by
// checking if passes to within a bounding box
bool insideFlag = true; // Whether viewPos is inside bounding box
double minDistBack = DBL_MAX; // min. distance to a backplane bounding the box
double maxDistFront= -DBL_MAX; // mix. distance to a frontplane bounding the box
double pdotn;
double alpha;
pdotn = (viewPos^AxisC) - CenterCoefC;
alpha = viewDir^AxisC;
if ( !CollideTwoPlanes(pdotn, alpha, MinorRadius,
&insideFlag, &minDistBack, &maxDistFront) ) {
return false;
}
pdotn = (viewPos^AxisA) - CenterCoefA;
alpha = viewDir^AxisA;
if ( !CollideTwoPlanes(pdotn, alpha, OuterRadius,
&insideFlag, &minDistBack, &maxDistFront) ) {
return false;
}
pdotn = (viewPos^AxisB) - CenterCoefB;
alpha = viewDir^AxisB;
if ( !CollideTwoPlanes(pdotn, alpha, OuterRadius,
&insideFlag, &minDistBack, &maxDistFront) ) {
return false;
}
assert ( minDistBack>=maxDistFront );
assert ( insideFlag || maxDistFront>=0.0 );
assert ( maxDistFront < 1000.0 );
if (maxDistFront>maxDistance) {
return false;
}
// Bounding box precheck is done. Now do the actual intersection test.
// Set up the degree 4 polynomial for the torus intersection
// Coefficients are:
// A = 1
// B = 4 u \cdot p
// C = 4(u\cdot p)^2 + 2(p\cdot p) - 2(M^2+m^2) + 4M^2(u_C \cdot u)
// D = 4[(p \cdot p)(u \cdot p) - (M^2+m^2)(u \cdot p) + 2M^2(u_C \dot p)^2]
// E = ((p \cdot p)^2 - 2(M^2+m^2)(p \cdot p) + 4M^2(u_C\cdot p)^2 +(M^2-m^2)^2
double moveFwdDist = Max(0.0,maxDistFront);
double coefs[5];
double roots[4];
double &A=coefs[0], &B=coefs[1], &C=coefs[2], &D=coefs[3], &E=coefs[4];
A = 1;
VectorR3 viewPosRel;
viewPosRel = viewDir;
viewPosRel *= moveFwdDist; // Move forward distance moveFwdDist
viewPosRel += viewPos;
viewPosRel -= Center; // Position relative to center
double udotp = (viewDir^viewPosRel);
B = 4.0*udotp;
double MSq = Square(MajorRadius);
double mSq = Square(MinorRadius);
double RadiiSqSum = MSq + mSq;
double ucdotp = (AxisC^viewPosRel);
double ucdotu = (AxisC^viewDir);
double pSq = (viewPosRel^viewPosRel);
C = 4.0*udotp*udotp + 2.0*pSq - 2.0*RadiiSqSum + 4.0*MSq*ucdotu*ucdotu;
D = 4.0 * ( (pSq-RadiiSqSum)*udotp + 2.0*MSq*ucdotp*ucdotu );
E = (pSq - 2.0*RadiiSqSum)*pSq + 4.0*MSq*ucdotp*ucdotp + Square(MSq-mSq);
int numRoots = PolySolveReal( 4, coefs, roots );
for ( int i=0; i<numRoots; i++ ) {
roots[i] += moveFwdDist; // Restate as distance from viewPos
if ( roots[i] >= maxDistance ) {
return false;
}
if ( roots[i]>0.0 ) {
// Return this visible point
*intersectDistance = roots[i];
VectorR3 Point = viewDir;
Point *= roots[i];
Point += viewPos;
returnedPoint.SetPosition(Point); // Intersection position (not relative to center)
if ( i & 0x01 ) {
returnedPoint.SetBackFace(); // Orientation
returnedPoint.SetMaterial( *InnerMaterial ); // Material
}
else {
returnedPoint.SetFrontFace(); // Orientation
returnedPoint.SetMaterial( *OuterMaterial ); // Material
}
// Outward normal
Point -= Center; // Now its the relative point
double xCoord = Point^AxisA; // forward axis
double yCoord = Point^AxisB; // rightward axis
double zCoord = Point^AxisC; // upward axis
VectorR3 outN = AxisC;
outN *= -zCoord;
outN += Point; // Project point down to plane of torus center
double outNnorm = outN.Norm();
outN *= MajorRadius/(-outNnorm); // Negative point projected to center path of torus
outN += Point; // Displacement of point from center path of torus
outN /= MinorRadius; // Should be outward unit vector
outN.ReNormalize(); // Fix roundoff error problems
returnedPoint.SetNormal(outN); // Outward normal
// u - v coordinates
double u = atan2( yCoord, xCoord );
u = u*PI2inv+0.5;
double bVal = outNnorm-MajorRadius;
double v = atan2( zCoord, bVal );
v = v*PI2inv+0.5;
returnedPoint.SetUV(u , v);
returnedPoint.SetFaceNumber( 0 );
return true;
}
}
return false;
}
