// cone sliced with vertical plane results in a hyperbola as the intersection curve
// find point where hyperbola and line slopes match
CC_CLZ_Pair ConeCutter::singleEdgeDropCanonical( const Point& u1, const Point& u2) const {
double d = u1.y;
double m = (u2.z-u1.z) / (u2.x-u1.x); // slope of edge
// the outermost point on the cutter is at xu = sqrt( R^2 - d^2 )
double xu = sqrt( square(radius) - square(u1.y) ); assert( xu <= radius );
// max slope at xu is mu = (L/(R-R2)) * xu /(sqrt( xu^2 + d^2 ))
double mu = (center_height/radius ) * xu / sqrt( square(xu) + square(d) ) ;
bool hyperbola_case = (fabs(m) <= fabs(mu));
// find contact point where slopes match, there are two cases:
// 1) if abs(m) <= abs(mu) we contact the curve at xp = sign(m) * sqrt( R^2 m^2 d^2 / (h^2 - R^2 m^2) )
// 2) if abs(m) > abs(mu) there is contact with the circular edge at +/- xu
double ccu;
if ( hyperbola_case ) {
ccu = sign(m) * sqrt( square(radius)*square(m)*square(d) / (square(length) -square(radius)*square(m) ) );
} else {
ccu = sign(m)*xu;
}
Point cc_tmp( ccu, d, 0.0); // cc-point in the XY plane
cc_tmp.z_projectOntoEdge(u1,u2);
double cl_z;
if ( hyperbola_case ) { // 1) zc = zp - Lc + (R - sqrt(xp^2 + d^2)) / tan(beta2)
cl_z = cc_tmp.z - center_height + (radius-sqrt(square(ccu) + square(d)))/ tan(angle);
} else { // 2) zc = zp - Lc
cl_z = cc_tmp.z - center_height; // case where we hit the edge of the cone
}
return CC_CLZ_Pair( ccu , cl_z);
}
// drop-cutter: Toroidal cutter edge-test
CC_CLZ_Pair BullCutter::singleEdgeDropCanonical( const Point& u1, const Point& u2 ) const {
if ( isZero_tol( u1.z - u2.z ) ) { // horizontal edge special case
return CC_CLZ_Pair( 0 , u1.z - height(u1.y) );
} else { // the general offset-ellipse case
double b_axis = radius2; // short axis of ellipse = radius2
double theta = atan( (u2.z - u1.z) / (u2.x-u1.x) ); // theta is the slope of the line
double a_axis = fabs( radius2/sin(theta) ); // long axis of ellipse = radius2/sin(theta)
Point ellcenter(0,u1.y,0);
Ellipse e = Ellipse( ellcenter, a_axis, b_axis, radius1);
int iters = e.solver_brent();
assert( iters < 200 );
e.setEllipsePositionHi(u1,u2); // this selects either EllipsePosition1 or EllipsePosition2 and sets it to EllipsePosition_hi
// pseudo cc-point on the ellipse/cylinder, in the CL=origo system
Point ell_ccp = e.ePointHi(); assert( fabs( ell_ccp.xyNorm() - radius1 ) < 1E-5); // ell_ccp should be on the cylinder-circle
Point cc_tmp_u = ell_ccp.closestPoint(u1,u2); // find real cc-point
return CC_CLZ_Pair( cc_tmp_u.x , e.getCenterZ()-radius2);
}
}
CC_CLZ_Pair CylCutter::singleEdgeDropCanonical(const Point& u1, const Point& u2) const {
// along the x-axis the cc-point is at x-coord s:
double s = sqrt( square( radius ) - square( u1.y ) );
Point cc1( s, u1.y, 0);
Point cc2( -s, u1.y, 0);
cc1.z_projectOntoEdge(u1,u2);
cc2.z_projectOntoEdge(u1,u2);
// pick the higher one
double cc_u;
double cl_z;
if (cc1.z > cc2.z) {
cc_u = cc1.x;
cl_z = cc1.z;
} else {
cc_u = cc2.x;
cl_z = cc2.z;
}
return CC_CLZ_Pair( cc_u, cl_z);
}
