/// find an intersection point in the XY-plane between two lines
/// first line: p1 + v*(p2-p1)
/// second line: p3 + t*(p4-p3)
/// sets (v,t) to the intersection point and returns true if an intersection was found
bool xy_line_line_intersection( const Point& p1, const Point& p2, double& v,
const Point& p3, const Point& p4, double& t) {
// p1 + v*(p2-p1) = p3 + t*(p4-p3)
// =>
// [ (p2-p1).x -(p4-p3).x ] [ v ] = [ (p3-p1).x ]
// [ (p2-p1).y -(p4-p3).y ] [ t ] = [ (p3-p1).y ]
return two_by_two_solver( (p2-p1).x , -(p4-p3).x , (p2-p1).y , -(p4-p3).y, (p3-p1).x, (p3-p1).y, v, t);
}
// general purpose facetPush
bool MillingCutter::generalFacetPush(double normal_length,
double center_height,
double xy_normal_length,
const Fiber& fib,
Interval& i,
const Triangle& t)
const {
bool result = false;
Point normal = t.upNormal(); // facet surface normal, pointing up
if ( normal.zParallel() ) // normal points in z-dir
return result; //can't push against horizontal plane, stop here.
normal.normalize();
Point xy_normal = normal;
xy_normal.z = 0;
xy_normal.xyNormalize();
// find a point on the plane from which radius2*normal+radius1*xy_normal lands on the fiber+radius2*Point(0,0,1)
// (u,v) locates a point on the triangle facet v0+ u*(v1-v0)+v*(v2-v0) u,v in [0,1]
// t locates a point along the fiber: p1 + t*(p2-p1) t in [0,1]
//
// facet-point + r2 * n + r1* xy_n = fiber-point + r2*Point(0,0,1)
// =>
// v0+ u*(v1-v0)+v*(v2-v0) + r2 * n + r1* xy_n = p1 + t*(p2-p1) + r2*Point(0,0,1)
//
// v0x + u*(v1x-v0x) + v*(v2x-v0x) + r2*nx + r1*xy_n.x = p1x + t*(p2x-p1x) p2x-p1x==0 for Y-fiber
// v0y + u*(v1y-v0y) + v*(v2y-v0y) + r2*ny + r1*xy_n.y = p1y + t*(p2y-p1y) p2y-p1y==0 for X-fiber
// v0z + u*(v1z-v0z) + v*(v2z-v0z) + r2*nz = p1z + t*(p2z-p1z) + r2 (p2z-p1z)==0 for XY-fibers!!
// X-fiber:
// v0x + u*(v1x-v0x) + v*(v2x-v0x) + r2*nx + r1*xy_n.x = p1x + t*(p2x-p1x)
// v0y + u*(v1y-v0y) + v*(v2y-v0y) + r2*ny + r1*xy_n.y = p1y solve these two for (u,v)
// v0z + u*(v1z-v0z) + v*(v2z-v0z) + r2*nz = p1z + r2 and substitute above for t
// or
// [ (v1y-v0y) (v2y-v0y) ] [ u ] = [ -v0y - r2*ny - r1*xy_n.y + p1y ]
// [ (v1z-v0z) (v2z-v0z) ] [ v ] = [ -v0z - r2*nz + p1z + r2 ]
//
// Y-fiber:
// [ (v1x-v0x) (v2x-v0x) ] [ u ] = [ -v0x - r2*nx - r1*xy_n.x + p1x ]
double a;
double b;
double c = t.p[1].z - t.p[0].z;
double d = t.p[2].z - t.p[0].z;
double e;
double f = -t.p[0].z - normal_length*normal.z + fib.p1.z + center_height;
// note: the xy_normal does not have a z-component, so omitted here.
double u, v; // u and v are coordinates of the cc-point within the triangle facet
// a,b,e depend on the fiber:
if ( fib.p1.y == fib.p2.y ) { // XFIBER
a = t.p[1].y - t.p[0].y;
b = t.p[2].y - t.p[0].y;
e = -t.p[0].y - normal_length*normal.y - xy_normal_length*xy_normal.y + fib.p1.y;
if (!two_by_two_solver(a,b,c,d,e,f,u,v))
return result;
CCPoint cc = t.p[0] + u*(t.p[1]-t.p[0]) + v*(t.p[2]-t.p[0]);
cc.type = FACET;
if ( ! cc.isInside( t ) )
return result;
// v0x + u*(v1x-v0x) + v*(v2x-v0x) + r2*nx + r1*xy_n.x = p1x + t*(p2x-p1x)
// =>
// t = 1/(p2x-p1x) * ( v0x + r2*nx + r1*xy_n.x - p1x + u*(v1x-v0x) + v*(v2x-v0x) )
assert( !isZero_tol( fib.p2.x - fib.p1.x ) ); // guard against division by zero
double tval = (1.0/( fib.p2.x - fib.p1.x )) * ( t.p[0].x + normal_length*normal.x + xy_normal_length*xy_normal.x - fib.p1.x
+ u*(t.p[1].x-t.p[0].x)+v*(t.p[2].x-t.p[0].x) );
if ( tval < 0.0 || tval > 1.0 ) {
std::cout << "MillingCutter::facetPush() tval= " << tval << " error!?\n";
//std::cout << " cutter: " << *this << "\n";
std::cout << " triangle: " << t << "\n";
std::cout << " fiber: " << fib << "\n";
}
assert( tval > 0.0 && tval < 1.0 );
i.update( tval, cc );
result = true;
} else if (fib.p1.x == fib.p2.x) { // YFIBER
a = t.p[1].x - t.p[0].x;
b = t.p[2].x - t.p[0].x;
e = -t.p[0].x - normal_length*normal.x - xy_normal_length*xy_normal.x + fib.p1.x;
if (!two_by_two_solver(a,b,c,d,e,f,u,v))
return result;
CCPoint cc = t.p[0] + u*(t.p[1]-t.p[0]) + v*(t.p[2]-t.p[0]);
cc.type = FACET;
if ( ! cc.isInside( t ) )
return result;
assert( !isZero_tol( fib.p2.y - fib.p1.y ) );
double tval = (1.0/( fib.p2.y - fib.p1.y )) * ( t.p[0].y + normal_length*normal.y + xy_normal_length*xy_normal.y - fib.p1.y
+ u*(t.p[1].y-t.p[0].y)+v*(t.p[2].y-t.p[0].y) );
if ( tval < 0.0 || tval > 1.0 ) {
std::cout << "MillingCutter::facetPush() tval= " << tval << " error!?\n";
std::cout << " (most probably a user error, the fiber is too short compared to the STL model?)\n";
}
assert( tval > 0.0 && tval < 1.0 );
i.update( tval, cc );
result = true;
} else {
assert(0);
}
return result;
}
