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opennurbs_intersect.cpp
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//
// Copyright (c) 1993-2022 Robert McNeel & Associates. All rights reserved.
// OpenNURBS, Rhinoceros, and Rhino3D are registered trademarks of Robert
// McNeel & Associates.
//
// THIS SOFTWARE IS PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY.
// ALL IMPLIED WARRANTIES OF FITNESS FOR ANY PARTICULAR PURPOSE AND OF
// MERCHANTABILITY ARE HEREBY DISCLAIMED.
//
// For complete openNURBS copyright information see <http://www.opennurbs.org>.
//
////////////////////////////////////////////////////////////////
#include "opennurbs.h"
#if !defined(ON_COMPILING_OPENNURBS)
// This check is included in all opennurbs source .c and .cpp files to insure
// ON_COMPILING_OPENNURBS is defined when opennurbs source is compiled.
// When opennurbs source is being compiled, ON_COMPILING_OPENNURBS is defined
// and the opennurbs .h files alter what is declared and how it is declared.
#error ON_COMPILING_OPENNURBS must be defined when compiling opennurbs
#endif
bool ON_IntersectLineLine(
const ON_Line& lineA,
const ON_Line& lineB,
double* a,
double* b,
double tolerance,
bool bIntersectSegments
)
{
bool rc = ON_Intersect(lineA,lineB,a,b) ? true : false;
if (rc)
{
if ( bIntersectSegments )
{
if ( *a < 0.0 )
*a = 0.0;
else if ( *a > 1.0 )
*a = 1.0;
if ( *b < 0.0 )
*b = 0.0;
else if ( *b > 1.0 )
*b = 1.0;
}
if ( tolerance > 0.0 )
{
rc = (lineA.PointAt(*a).DistanceTo(lineB.PointAt(*b)) <= tolerance);
}
}
return rc;
}
bool ON_Intersect( const ON_BoundingBox& bbox,
const ON_Line& line,
double tol,
ON_Interval* line_parameters)
{
double a,b,d,mn,mx,s0,s1, t0, t1;
const double M = 1.0e308;
// i,j,k are indices of coordinates to trim.
// trim the direction with the biggest line deltas first
ON_3dVector v = line.Direction();
const int i = v.MaximumCoordinateIndex();
// guard against ON_UNSET_VALUE as input
if ( !(tol >= 0.0) )
tol = 0.0;
// clip i-th coordinate
a = line.from[i];
b = line.to[i];
mn = bbox.m_min[i];
mx = bbox.m_max[i];
if ( !(mn <= mx) )
return false;
mn -= (tol+a);
mx += (tol-a);
if ( !(mn <= mx) )
return false;
d = b-a;
if ( 0.0 == d )
{
// happens when line.from == line.to
if ( 0.0 < mn || 0.0 > mx )
{
// point is in box
if ( line_parameters )
{
// setting parameters makes no sense - just use 0.0
// so it's clear we have a point
line_parameters->Set(0.0,0.0);
}
return true;
}
return false; // point is outside box
}
if ( fabs(d) < 1.0 && (fabs(mn) >= fabs(d)*M || fabs(mx) >= fabs(d)*M) )
{
// the value of mn/d or mx/d is too large for a realistic answer to be computed
return false;
}
d = 1.0/d;
t0 = mn*d;
t1 = mx*d;
// set "chord" = line segment that begins and ends on the
// i-th coordinate box side planes.
ON_Line chord(line.PointAt(t0),line.PointAt(t1));
// test j-th coordinate direction
const int j = (i + (fabs(v[(i+1)%3])>fabs(v[(i+2)%3])?1:2) ) % 3;
a = chord.from[j];
b = chord.to[j];
mn = bbox.m_min[j];
mx = bbox.m_max[j];
if ( !(mn <= mx) )
return false;
mn -= (tol+a);
mx += (tol-a);
if ( !(mn <= mx) )
return false;
d = b-a;
if ( (0.0 < mn && d < mn) || (0.0 > mx && d > mx) )
{
// chord lies outside the box
return false;
}
while ( fabs(d) >= 1.0 || (fabs(mn) <= fabs(d)*M && fabs(mx) <= fabs(d)*M) )
{
// The chord is not (nearly) parallel to the j-th sides.
// See if the chord needs to be trimmed by the j-th sides.
d = 1.0/d;
s0 = mn*d;
s1 = mx*d;
if ( s0 > 1.0 )
{
if ( s1 > 1.0 )
{
// unstable calculation happens when
// fabs(d) is very tiny and chord is
// on the j-th side.
break;
}
s0 = 1.0;
}
else if ( s0 < 0.0 )
{
if (s1 < 0.0)
{
// unstable calculation happens when
// fabs(d) is very tiny and chord is
// on the j-th side.
break;
}
s0 = 0.0;
}
if ( s1 < 0.0 ) s1 = 0.0; else if ( s1 > 1.0 ) s1 = 1.0;
d = (1.0-s0)*t0 + s0*t1;
t1 = (1.0-s1)*t0 + s1*t1;
t0 = d;
v = chord.PointAt(s0);
chord.to = chord.PointAt(s1);
chord.from = v;
break;
}
// test k-th coordinate direction
const int k = (i&&j) ? 0 : ((i!=1&&j!=1)?1:2);
a = chord.from[k];
b = chord.to[k];
mn = bbox.m_min[k];
mx = bbox.m_max[k];
if ( !(mn <= mx) )
return false;
mn -= (tol+a);
mx += (tol-a);
if ( !(mn <= mx) )
return false;
d = b-a;
if ( (0.0 < mn && d < mn) || (0.0 > mx && d > mx) )
{
// chord does not intersect the rectangle
return false;
}
if ( line_parameters )
{
while ( fabs(d) >= 1.0 || (fabs(mn) <= fabs(d)*M && fabs(mx) <= fabs(d)*M) )
{
// The chord is not (nearly) parallel to the k-th sides.
// See if the chord needs to be trimmed by the k-th sides.
d = 1.0/d;
s0 = mn*d;
s1 = mx*d;
if ( s0 > 1.0 )
{
if ( s1 > 1.0 )
{
// unstable calculation happens when
// fabs(d) is very tiny and chord is
// on the k-th side.
break;
}
s0 = 1.0;
}
else if ( s0 < 0.0 )
{
if (s1 < 0.0)
{
// unstable calculation happens when
// fabs(d) is very tiny and chord is
// on the k-th side.
break;
}
s0 = 0.0;
}
if ( s1 < 0.0 ) s1 = 0.0; else if ( s1 > 1.0 ) s1 = 1.0;
d = (1.0-s0)*t0 + s0*t1;
t1 = (1.0-s1)*t0 + s1*t1;
t0 = d;
break;
}
if (t0 > t1 )
{
line_parameters->Set(t1,t0);
}
else
{
line_parameters->Set(t0,t1);
}
}
return true;
}
bool ON_Intersect( const ON_Line& lineA, const ON_Line& lineB,
double* lineA_parameter,
double* lineB_parameter
)
{
// If you are looking at this code because you don't like an
// answer you are getting, then the first thing to try is
// to read the header file comments and try calling
// ON_IntersectLineLine.
bool rc = false;
double M_zero_tol = 0.0;
int i, rank;
double pr_tolerance, pivot, X[2], Y[2];
ON_3dVector A = lineA.Direction();
ON_3dVector B = lineB.Direction();
ON_3dVector C = lineB[0] - lineA[0];
ON_Matrix M(2,2);
M[0][0] = ON_DotProduct( A, A );
M[1][1] = ON_DotProduct( B, B );
M[0][1] = M[1][0] = -ON_DotProduct( A, B );
// this swap done to get row+col pivot accuracy
if ( M[0][0] < M[1][1] ) {
M.SwapCols(0,1);
i = 1;
}
else {
i = 0;
}
// 2021-07-21, Pierre, RH-65014
// It does not make much sense to use a tolerance lower than ON_EPSILON on the
// result of arithmetic on doubles. If M[1][1] is smaller than 1, we need to
// bound M_zero_tol to ON_EPSILON or ON_Intersect will wrongly return true on
// many near-parallel cases. pr_tolerance also needs to be bounded as it
// cannot be smaller than M_zero_tolerance.
//
// Before that change, lines
// Line A = (5.4301839655138417, -9.5, 0, -0.6, -9.5, 0)
// Line B = (5.2373595635311068, 10.5, 0, 5.6603292194932395, 10.5, 0)
// would be found as intersecting, with pivot ~= 2 * M_zero_tolerance
if (fabs(M[1][1]) > 1.) {
pr_tolerance = fabs(M[1][1]) * ON_SQRT_EPSILON;
M_zero_tol = fabs(M[1][1]) * ON_EPSILON;
} else {
pr_tolerance = ON_SQRT_EPSILON;
M_zero_tol = ON_EPSILON;
}
Y[0] = ON_DotProduct( A, C );
Y[1] = -ON_DotProduct( B, C );
rank = M.RowReduce( M_zero_tol, Y, &pivot );
if ( rank == 2 )
{
// 19 November 2003 Dale Lear and Chuck
// Added lineA.from/to == lineB.from/to tests
// so exact answer gets returned when people
// expect it.
rc = true;
if ( lineA.from == lineB.from )
{
if ( lineA_parameter )
*lineA_parameter = 0.0;
if ( lineB_parameter )
*lineB_parameter = 0.0;
}
else if ( lineA.from == lineB.to )
{
if ( lineA_parameter )
*lineA_parameter = 0.0;
if ( lineB_parameter )
*lineB_parameter = 1.0;
}
else if ( lineA.to == lineB.from )
{
if ( lineA_parameter )
*lineA_parameter = 1.0;
if ( lineB_parameter )
*lineB_parameter = 0.0;
}
else if ( lineA.to == lineB.to )
{
if ( lineA_parameter )
*lineA_parameter = 1.0;
if ( lineB_parameter )
*lineB_parameter = 1.0;
}
else
{
rc = M.BackSolve( 0.0, 2, Y, X );
if ( rc )
{
if ( lineA_parameter )
*lineA_parameter = X[i];
if ( lineB_parameter )
*lineB_parameter = X[1-i];
if ( fabs(pivot) <= pr_tolerance )
{
// test answer because matrix was close to singular
// (This test is slow but it is rarely used.)
ON_3dPoint pA = lineA.PointAt(X[i]);
ON_3dPoint pB = lineB.PointAt(X[1-i]);
double d = pA.DistanceTo(pB);
if ( d > pr_tolerance && d > ON_ZERO_TOLERANCE ) {
ON_3dPoint qA = lineA.ClosestPointTo(pB);
ON_3dPoint qB = lineB.ClosestPointTo(pA);
double dA = pA.DistanceTo(qB);
double dB = pB.DistanceTo(qA);
if ( 1.1*dA < d ) {
rc = false;
}
else if ( 1.1*dB < d ) {
rc = false;
}
}
}
}
}
}
return rc;
}
bool ON_Intersect(
const ON_Line& line,
const ON_PlaneEquation& plane_equation,
double* line_parameter
)
{
bool rc = false;
double a, b, d, fd, t;
a = plane_equation.ValueAt(line.from);
b = plane_equation.ValueAt(line.to);
d = a-b;
if ( d == 0.0 )
{
if ( fabs(a) < fabs(b) )
t = 0.0;
else if ( fabs(b) < fabs(a) )
t = 1.0;
else
t = 0.5;
}
else
{
d = 1.0/d;
fd = fabs(d);
if ( fd > 1.0 && (fabs(a) >= ON_DBL_MAX/fd || fabs(b) >= ON_DBL_MAX/fd ) )
{
// double overflow - line may be (nearly) parallel to plane
t = 0.5;
}
else
{
t = a/(a-b); // = a*d; a/(a-b) has more precision than a*d
rc = true;
}
}
if ( line_parameter )
*line_parameter = t;
return rc;
}
bool ON_Intersect(
const ON_Line& line,
const ON_Plane& plane,
double* line_parameter
)
{
return ON_Intersect( line, plane.plane_equation, line_parameter );
}
bool ON_Intersect( const ON_Plane& R, const ON_Plane& S,
ON_Line& L )
{
ON_3dVector d = ON_CrossProduct( S.zaxis, R.zaxis );
ON_3dPoint p = 0.5*(R.origin + S.origin);
ON_Plane T( p, d );
bool rc = ON_Intersect( R, S, T, L.from );
L.to = L.from + d;
return rc;
}
bool ON_Intersect( const ON_Plane& R, const ON_Plane& S, const ON_Plane& T,
ON_3dPoint& P )
{
double pr = 0.0;
const int rank = ON_Solve3x3(
&R.plane_equation.x, &S.plane_equation.x, &T.plane_equation.x,
-R.plane_equation.d, -S.plane_equation.d, -T.plane_equation.d,
&P.x, &P.y, &P.z, &pr );
return (rank == 3) ? true : false;
}
int ON_Intersect(
const ON_Plane& plane,
const ON_Sphere& sphere,
ON_Circle& circle
)
{
// 16 April 2011 Dale Lear
// Prior to this date, this function did not return the correct answer.
int rc = 0;
const double sphere_radius = fabs(sphere.radius);
double tol = sphere_radius*ON_SQRT_EPSILON;
if ( !(tol >= ON_ZERO_TOLERANCE) )
tol = ON_ZERO_TOLERANCE;
const ON_3dPoint sphere_center = sphere.Center();
ON_3dPoint circle_center = plane.ClosestPointTo(sphere_center);
double d = circle_center.DistanceTo(sphere_center);
circle.radius = 0.0;
if ( ON_IsValid(sphere_radius) && ON_IsValid(d) && d <= sphere_radius + tol )
{
if ( sphere_radius > 0.0 )
{
d /= sphere_radius;
d = 1.0 - d*d;
// The d > 4.0*ON_EPSILON was picked by testing spheres with
// radius = 1 and center = (0,0,0). Do not make 4.0*ON_EPSILON
// any smaller and please discuss changes with Dale Lear.
circle.radius = (d > 4.0*ON_EPSILON) ? sphere_radius*sqrt(d) : 0.0;
}
else
circle.radius = 0.0;
if ( circle.radius <= ON_ZERO_TOLERANCE )
{
// return a single point
rc = 1;
circle.radius = 0.0;
// When tolerance is in play, put the point on the sphere.
// If the caller prefers the plane, then they can adjust the
// returned answer to get the plane.
ON_3dVector R = circle_center - sphere_center;
double r0 = R.Length();
if ( r0 > 0.0 )
{
R.Unitize();
ON_3dPoint C1 = sphere_center + sphere_radius*R;
double r1 = C1.DistanceTo(sphere_center);
if ( fabs(sphere.radius-r1) < fabs(sphere.radius-r0) )
circle_center = C1;
}
}
else
{
// return a circle
rc = 2;
}
}
// Update circle's plane here in case the input plane
// is the circle's plane member.
circle.plane = plane;
circle.plane.origin = circle_center;
circle.plane.UpdateEquation();
return rc;
}
int ON_Intersect(
const ON_Line& line,
const ON_Sphere& sphere,
ON_3dPoint& A,
ON_3dPoint& B // intersection point(s) returned here
)
{
int rc = 0;
const ON_3dPoint sphere_center = sphere.plane.origin;
const double sphere_radius = fabs(sphere.radius);
double tol = sphere_radius*ON_SQRT_EPSILON;
if ( tol < ON_ZERO_TOLERANCE )
tol = ON_ZERO_TOLERANCE;
ON_3dPoint line_center = line.ClosestPointTo(sphere_center);
double d = line_center.DistanceTo(sphere_center);
if ( d >= sphere_radius-tol ) {
rc = ( d <= sphere_radius-tol ) ? 1 : 0;
A = line_center;
B = sphere.ClosestPointTo(line_center);
}
else {
d /= sphere_radius;
double h = sphere_radius*sqrt(1.0 - d*d);
ON_3dVector V = line.Direction();
V.Unitize();
A = sphere.ClosestPointTo(line_center - h*V);
B = sphere.ClosestPointTo(line_center + h*V);
d = A.DistanceTo(B);
if ( d <= ON_ZERO_TOLERANCE ) {
A = line_center;
B = sphere.ClosestPointTo(line_center);
rc = 1;
}
else
rc = 2;
}
return rc;
}
static
int Intersect2dLineCircle(
ON_2dPoint line_from, // 2d line from point
ON_2dPoint line_to,
double r,
double tol,
double* t0,
double* t1
)
{
// returns 0 = line is degenerate
// 1 = one intersection returned,
// 2 = 2 intersections returned
// 3 = 1 closest point returned
int xcnt = 0;
bool bRev;
double t, d, c, s, x, y, dx, dy;
ON_2dVector v;
if ( line_from.x*line_from.x + line_from.y*line_from.y > line_to.x*line_to.x + line_to.y*line_to.y )
{
v = line_from;
line_from = line_to;
line_to = v;
bRev = true;
}
else
bRev = false;
dx = line_to.x - line_from.x;
dy = line_to.y - line_from.y;
if ( fabs(dx) >= fabs(dy) )
{
if ( dx == 0.0 )
{
*t0 = 0.0;
*t1 = 0.0;
return 0;
}
else
{
d = dy/dx;
d = fabs(dx)*sqrt(1.0+d*d);
}
}
else
{
d = dx/dy;
d = fabs(dy)*sqrt(1.0+d*d);
}
c = dx/d;
s = dy/d;
// change coordinates so line is horizontal
x = line_from.x;
y = line_from.y;
line_from.x = c*x + s*y;
line_from.y = c*y - s*x;
x = line_to.x;
y = line_to.y;
line_to.x = c*x + s*y;
line_to.y = c*y - s*x;
dx = line_to.x - line_from.x; // should be length of line
if ( dx == 0.0 )
{
*t0 = 0.0;
*t1 = 0.0;
return 0;
}
dy = line_to.y - line_from.y; // should be zero
t = -line_from.x/dx;
x = (1.0-t)*line_from.x + t*line_to.x;
y = (1.0-t)*line_from.y + t*line_to.y;
d = fabs(y);
if ( d < r-tol )
{
// two intersection points
d /= r;
d = r*sqrt(1.0-d*d);
x = -(d + line_from.x)/dx;
y = (d - line_from.x)/dx;
if ( bRev )
{
x = 1.0-x;
y = 1.0-y;
}
if (x<=y)
{
*t0 = x;
*t1 = y;
}
else
{
*t0 = y;
*t1 = x;
}
xcnt = ( x == y ) ? 1 : 2;
}
else if ( d > r+tol )
{
// closest point returned
xcnt = 3;
if ( bRev )
t = 1.0-t;
*t0 = t;
*t1 = t;
}
else
{
// one intersection point returned
xcnt = 1;
if ( bRev )
t = 1.0-t;
*t0 = t;
*t1 = t;
}
return xcnt;
}
int ON_Intersect(
const ON_Line& line,
const ON_Cylinder& cylinder, // if cylinder.height[0]==cylinder.height[1],
// then infinite cyl is used. Otherwise
// finite cyl is used.
ON_3dPoint& A, ON_3dPoint& B // intersection point(s) returned here
)
{
bool bFiniteCyl = true;
int rc = 0;
const double cylinder_radius = fabs(cylinder.circle.radius);
double tol = cylinder_radius*ON_SQRT_EPSILON;
if ( tol < ON_ZERO_TOLERANCE )
tol = ON_ZERO_TOLERANCE;
ON_Line axis;
axis.from = cylinder.circle.plane.origin + cylinder.height[0]*cylinder.circle.plane.zaxis;
axis.to = cylinder.circle.plane.origin + cylinder.height[1]*cylinder.circle.plane.zaxis;
if ( axis.Length() <= tol ) {
axis.to = cylinder.circle.plane.origin + cylinder.circle.plane.zaxis;
bFiniteCyl = false;
}
//bool bIsParallel = false;
double line_t, axis_t;
if ( !ON_Intersect(line,axis,&line_t,&axis_t) ) {
axis.ClosestPointTo( cylinder.circle.plane.origin, &axis_t );
line.ClosestPointTo( cylinder.circle.plane.origin, &line_t );
}
ON_3dPoint line_point = line.PointAt(line_t);
ON_3dPoint axis_point = axis.PointAt(axis_t);
double d = line_point.DistanceTo(axis_point);
if ( bFiniteCyl ) {
if ( axis_t < 0.0 )
axis_t = 0.0;
else if ( axis_t > 1.0 )
axis_t = 1.0;
axis_point = axis.PointAt(axis_t);
}
if ( d >= cylinder_radius-tol) {
rc = ( d <= cylinder_radius+tol ) ? 1 : 0;
A = line_point;
ON_3dVector V = line_point - axis_point;
if ( bFiniteCyl ) {
V = V - (V*cylinder.circle.plane.zaxis)*cylinder.circle.plane.zaxis;
}
V.Unitize();
B = axis_point + cylinder_radius*V;
if ( rc == 1 ) {
// check for overlap
ON_3dPoint P = axis.ClosestPointTo(line.from);
d = P.DistanceTo(line.from);
if ( fabs(d-cylinder_radius) <= tol ) {
P = axis.ClosestPointTo(line.to);
d = P.DistanceTo(line.to);
if ( fabs(d-cylinder_radius) <= tol ) {
rc = 3;
A = cylinder.ClosestPointTo(line.from);
B = cylinder.ClosestPointTo(line.to);
}
}
}
}
else {
// transform to coordinate system where equation of cyl
// is x^2 + y^2 = R^2 and solve for line parameter(s).
ON_Xform xform;
xform.Rotation( cylinder.circle.plane, ON_xy_plane );
ON_Line L = line;
L.Transform(xform);
const double x0 = L.from.x;
const double x1 = L.to.x;
const double x1mx0 = x1-x0;
double ax = x1mx0*x1mx0;
double bx = 2.0*x1mx0*x0;
double cx = x0*x0;
const double y0 = L.from.y;
const double y1 = L.to.y;
const double y1my0 = y1-y0;
double ay = y1my0*y1my0;
double by = 2.0*y1my0*y0;
double cy = y0*y0;
double t0, t1;
int qerc = ON_SolveQuadraticEquation(ax+ay, bx+by, cx+cy-cylinder_radius*cylinder_radius,
&t0,&t1);
if ( qerc == 2 ) {
// complex roots - ignore (tiny) imaginary part caused by computational noise.
t1 = t0;
}
A = cylinder.ClosestPointTo(line.PointAt(t0));
B = cylinder.ClosestPointTo(line.PointAt(t1));
d = A.DistanceTo(B);
if ( d <= ON_ZERO_TOLERANCE ) {
A = line_point;
ON_3dVector V = line_point - axis_point;
if ( bFiniteCyl ) {
V = V - (V*cylinder.circle.plane.zaxis)*cylinder.circle.plane.zaxis;
}
V.Unitize();
B = axis_point + cylinder_radius*V;
rc = 1;
}
else
rc = 2;
}
return rc;
}
int ON_Intersect(
const ON_Line& line,
const ON_Circle& circle,
double* line_t0,
ON_3dPoint& circle_point0,
double* line_t1,
ON_3dPoint& circle_point1
)
{
// transform to coordinate system where equation of circle
// is x^2 + y^2 = R^2 and solve for line parameter(s).
ON_Xform xform;
xform.ChangeBasis( circle.plane, ON_xy_plane );
xform.ChangeBasis( ON_xy_plane, circle.plane );
ON_Line L = line;
L.Transform(xform);
double r = fabs(circle.radius);
double tol = (circle.Center().MaximumCoordinate()+ r)*ON_RELATIVE_TOLERANCE;
if ( tol < ON_ZERO_TOLERANCE )
tol = ON_ZERO_TOLERANCE;
int xcnt;
if ( fabs(L.from.x - L.to.x) <= tol
&& fabs(L.from.y - L.to.y) <= tol
&& fabs(L.from.z - L.to.z) > tol )
{
if (fabs(L.from.x * L.from.x + L.from.y * L.from.y - r*r) < tol)
{
*line_t0 = -L.from.z / (L.to.z - L.from.z);
xcnt = 1;
}
else
xcnt = 0;
}
else
{
xcnt = Intersect2dLineCircle( ON_2dPoint(L.from), ON_2dPoint(L.to), r, tol, line_t0, line_t1 );
if ( xcnt == 3 )
xcnt = 1;
}
int rcnt = 0; // actual number of intersections within tol
if (xcnt > 0)
{
ON_3dPoint line_point1, line_point0 = line.PointAt(*line_t0);
circle_point0 = circle.ClosestPointTo(line_point0);
bool x0 = circle_point0.IsCoincident(line_point0);
bool x1 = false;
if (xcnt == 2)
{
line_point1 = line.PointAt(*line_t1);
circle_point1 = circle.ClosestPointTo(line_point1);
x1 = circle_point1.IsCoincident(line_point1);
}
if(x0)
rcnt ++;
if (x1)
{
rcnt++;
if (rcnt == 1)
{
circle_point0 = circle_point1;
line_t0 = line_t1;
}
}
}
return rcnt;
}
int ON_Intersect(
const ON_Plane& plane,
const ON_Circle& circle,
ON_3dPoint& point0,
ON_3dPoint& point1
)
{
int rval = -1;
ON_Line xline;
double a,b;
bool rc = ON_Intersect(plane, circle.Plane(), xline);
if(rc)
{
rval = ON_Intersect(xline, circle, &a, point0, &b, point1);
}
else
{
double d = plane.plane_equation.ValueAt( circle.Center() );
if(d<ON_ZERO_TOLERANCE)
rval =3;
else
rval = 0;
}
return rval;
}
int ON_Intersect(
const ON_Plane& plane,
const ON_Arc& arc,
ON_3dPoint& point0,
ON_3dPoint& point1
)
{
int rval = -1;
ON_Line xline;
double a,b;
bool rc = ON_Intersect(plane, arc.Plane(), xline);
if(rc)
{
rval = ON_Intersect(xline, arc, &a, point0, &b, point1);
}
else
{
double d = plane.plane_equation.ValueAt( arc.StartPoint() );
if(d<ON_ZERO_TOLERANCE)
rval =3;
else
rval = 0;
}
return rval;
}
int ON_Intersect(
const ON_Circle& C0,
const ON_Circle& C1,
ON_3dPoint& P0,
ON_3dPoint& P1)
{
P0 = P1 = ON_3dPoint::UnsetPoint;
int xcnt = -1;
const double costol = ON_ZERO_TOLERANCE;
double scale0 = C0.MaximumCoordinate();
double abstol = C1.MaximumCoordinate();
if (abstol < scale0)
abstol = scale0;
abstol *= ON_RELATIVE_TOLERANCE;
if (abstol < ON_ZERO_TOLERANCE)
abstol = ON_ZERO_TOLERANCE;
bool parallel = (fabs(C0.plane.Normal() * C1.plane.Normal()) > 1 - costol); // todo pretty loose and insensitive
bool coplanar = parallel && (C0.plane.DistanceTo(C1.plane.origin) < abstol);
if (coplanar)
{
const ON_Circle* C[2] = { &C0, &C1 };
if (C1.Radius() >= C0.Radius())
{
C[0] = &C1;
C[1] = &C0;
}
double R0 = C[0]->Radius(); // largest radius
double R1 = C[1]->Radius();
ON_3dVector D = C[1]->Center() - C[0]->Center();
double d = D.Length();
if (d > abstol)
{
D.Unitize();
ON_3dVector Dperp = ON_CrossProduct(D, C[0]->Normal());
if (d > R0 + R1 + abstol)
xcnt = 0; // disks are disjoint
else if (d + R1 + abstol < R0)
xcnt = 0; // small disk is in interior of large disk
else
{
double d1 = (R0 * R0 - R1 * R1 + d * d) / (2 * d);
double a1 = R0 * R0 - d1 * d1;
if (a1 < 0)
a1 = 0;
a1 = sqrt(a1);
if (a1 < .5 * abstol)
{
xcnt = 1;
P0 = C[0]->Center() + d1 * D;
}
else
{
xcnt = 2;
P0 = C[0]->Center() + d1 * D + a1 * Dperp;
P1 = C[0]->Center() + d1 * D - a1 * Dperp;
}
}
}
else if (R0 - R1 < abstol)
xcnt = 3;
else
xcnt = 0;
}
else if (!parallel)