bool ON_Circle::Create( // circle through three 3d points
const ON_3dPoint& P,
const ON_3dPoint& Q,
const ON_3dPoint& R
)
{
ON_3dPoint C;
ON_3dVector X, Y, Z;
// return ( radius > 0.0 && plane.IsValid() );
//m_point[0] = P;
//m_point[1] = Q;
//m_point[2] = R;
// get normal
bool rc = Z.PerpendicularTo( P, Q, R );
// get center as the intersection of 3 planes
//
ON_Plane plane0( P, Z );
ON_Plane plane1( 0.5*(P+Q), P-Q );
ON_Plane plane2( 0.5*(R+Q), R-Q );
if ( !ON_Intersect( plane0, plane1, plane2, C ) )
rc = false;
X = P - C;
radius = X.Length();
if ( radius == 0.0 )
rc = false;
X.Unitize();
Y = ON_CrossProduct( Z, X );
Y.Unitize();
plane.origin = C;
plane.xaxis = X;
plane.yaxis = Y;
plane.zaxis = Z;
plane.UpdateEquation();
return rc;
}
static void
test_psi(ON_3dPoint &p, ON_Surface &s)
{
ON_wString wstr;
ON_TextLog textlog(wstr);
ON_ClassArray<ON_PX_EVENT> x;
// Use default tolerance
ON_Intersect(p, s, x);
// XXX: How to simply show a surface?
bu_log("(%f,%f,%f) and a surface:\n", p[0], p[1], p[2]);
if (x.Count() == 0) {
bu_log("No intersection.\n");
} else {
for (int i = 0; i < x.Count(); i++)
x[i].Dump(textlog);
ON_String str(wstr);
bu_log(str.Array());
}
bu_log("\n\n");
}
static void
test_ppi(ON_3dPoint &p1, ON_3dPoint &p2)
{
ON_wString wstr;
ON_TextLog textlog(wstr);
ON_ClassArray<ON_PX_EVENT> x;
// Use default tolerance
ON_Intersect(p1, p2, x);
bu_log("(%f,%f,%f) and (%f,%f,%f):\n", p1[0], p1[1], p1[2], p2[0], p2[1], p2[2]);
if (x.Count() == 0) {
bu_log("No intersection.\n");
} else {
for (int i = 0; i < x.Count(); i++)
x[i].Dump(textlog);
ON_String str(wstr);
bu_log(str.Array());
}
bu_log("\n\n");
}
double ON_Line::MinimumDistanceTo( const ON_Line& L ) const
{
ON_3dPoint A, B;
double a, b, t, x, d;
bool bCheckA, bCheckB;
bool bGoodX = ON_Intersect(*this,L,&a,&b);
bCheckA = true;
if ( a < 0.0) a = 0.0; else if (a > 1.0) a = 1.0; else bCheckA=!bGoodX;
bCheckB = true;
if ( b < 0.0) b = 0.0; else if (b > 1.0) b = 1.0; else bCheckB=!bGoodX;
A = PointAt(a);
B = L.PointAt(b);
d = A.DistanceTo(B);
if ( bCheckA )
{
L.ClosestPointTo(A,&t);
if (t<0.0) t = 0.0; else if (t > 1.0) t = 1.0;
x = L.PointAt(t).DistanceTo(A);
if ( x < d )
d = x;
}
if ( bCheckB )
{
ClosestPointTo(B,&t);
if (t<0.0) t = 0.0; else if (t > 1.0) t = 1.0;
x = PointAt(t).DistanceTo(B);
if (x < d )
d = x;
}
return d;
}
static void
test_pci(ON_3dPoint &p, ON_Curve &c)
{
ON_wString wstr;
ON_TextLog textlog(wstr);
ON_ClassArray<ON_PX_EVENT> x;
// Use default tolerance
ON_Intersect(p, c, x);
ON_3dPoint start = c.PointAtStart();
ON_3dPoint end = c.PointAtEnd();
bu_log("(%f,%f,%f) and [(%f,%f,%f) to (%f,%f,%f)]:\n",
p[0], p[1], p[2], start[0], start[1], start[2], end[0], end[1], end[2]);
if (x.Count() == 0) {
bu_log("No intersection.\n");
} else {
for (int i = 0; i < x.Count(); i++)
x[i].Dump(textlog);
ON_String str(wstr);
bu_log(str.Array());
}
bu_log("\n\n");
}
int ON_Intersect(
const ON_Line& line,
const ON_Arc& arc,
double* line_t0,
ON_3dPoint& arc_point0,
double* line_t1,
ON_3dPoint& arc_point1
)
{
ON_Circle c = arc;
ON_3dPoint p[2];
double t[2], a[2], s;
ON_BOOL32 b[2] = {false,false};
int i, xcnt = ON_Intersect( line, c, &t[0], p[0], &t[1], p[1] );
if ( xcnt > 0 )
{
// make sure points are on the arc;
ON_Interval arc_domain = arc.DomainRadians();
for ( i = 0; i < xcnt; i++ )
{
b[i] = c.ClosestPointTo(p[i], &a[i]);
if ( b[i] )
{
s = arc_domain.NormalizedParameterAt(a[i]);
if ( s < 0.0 )
{
if ( s >= -ON_SQRT_EPSILON )
{
a[i] = arc_domain[0];
p[i] = c.PointAt(a[i]);
b[i] = line.ClosestPointTo( p[i], &t[i] );
}
else
b[i] = false;
}
else if ( s > 1.0 )
{
if ( s <= 1.0+ON_SQRT_EPSILON )
{
a[i] = arc_domain[1];
p[i] = c.PointAt(a[i]);
b[i] = line.ClosestPointTo( p[i], &t[i] );
}
else
b[i] = false;
}
}
}
if ( !b[0] && !b[1] )
xcnt = 0;
if ( xcnt == 2 )
{
if ( !b[1] )
xcnt = 1;
if ( !b[0] )
{
xcnt = 1;
b[0] = b[1];
t[0] = t[1];
a[0] = a[1];
p[0] = p[1];
b[1] = 0;
}
if ( xcnt == 2 && t[0] == t[1] )
{
xcnt = 1;
b[1] = 0;
ON_3dPoint q = line.PointAt(t[0]);
if ( p[0].DistanceTo(q) > p[1].DistanceTo(q) )
{
a[0] = a[1];
t[0] = t[1];
p[0] = p[1];
}
}
}
if ( xcnt == 1 && !b[0] )
xcnt = 0;
if ( xcnt >= 1 )
{
if ( line_t0 )
*line_t0 = t[0];
arc_point0 = p[0];
}
if ( xcnt == 2 )
{
if ( line_t1 )
*line_t1 = t[1];
arc_point1 = p[1];
}
}
return xcnt;
}
int ON_Intersect( // returns 0 = no intersections,
// 1 = one intersection,
// 2 = 2 intersections
// 3 = line lies on cylinder
// If 0 is returned, first point is point
// on line closest to cylinder and 2nd point is the point
// on the sphere closest to the line.
// If 1 is returned, first point is obtained by evaluating
// the line and the second point is obtained by evaluating
// the cylinder.
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
)
{
ON_BOOL32 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;
}
//ON_BOOL32 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;
}
bool ON_Line::IsFartherThan( double d, const ON_Line& L ) const
{
ON_3dPoint A, B;
double a, b, t, x;
bool bCheckA, bCheckB;
a = from.x; if (to.x < a) {b=a; a = to.x;} else b = to.x;
if ( b+d < L.from.x && b+d < L.to.x )
return true;
if ( a-d > L.from.x && a-d > L.to.x )
return true;
a = from.y; if (to.y < a) {b=a; a = to.y;} else b = to.y;
if ( b+d < L.from.y && b+d < L.to.y )
return true;
if ( a-d > L.from.y && a-d > L.to.y )
return true;
a = from.z; if (to.z < a) {b=a; a = to.z;} else b = to.z;
if ( b+d < L.from.z && b+d < L.to.z )
return true;
if ( a-d > L.from.z && a-d > L.to.z )
return true;
if ( !ON_Intersect(*this,L,&a,&b) )
{
// lines are parallel or anti parallel
if ( Direction()*L.Direction() >= 0.0 )
{
// lines are parallel
a = 0.0;
L.ClosestPointTo(from,&b);
// If ( b >= 0.0), then this->from and L(b) are a pair of closest points.
if ( b < 0.0 )
{
// Othersise L.from and this(a) are a pair of closest points.
b = 0.0;
ClosestPointTo(L.from,&a);
}
}
else
{
// lines are anti parallel
a = 1.0;
L.ClosestPointTo(to,&b);
// If ( b >= 0.0), then this->to and L(b) are a pair of closest points.
if ( b < 0.0 )
{
// Othersise L.to and this(a) are a pair of closest points.
b = 0.0;
ClosestPointTo(L.from,&a);
}
}
}
A = PointAt(a);
B = L.PointAt(b);
x = A.DistanceTo(B);
if (x > d)
return true;
bCheckA = true;
if ( a < 0.0) a = 0.0; else if (a > 1.0) a = 1.0; else bCheckA=false;
if (bCheckA )
{
A = PointAt(a);
L.ClosestPointTo(A,&t);
if (t<0.0) t = 0.0; else if (t > 1.0) t = 1.0;
x = L.PointAt(t).DistanceTo(A);
}
bCheckB = true;
if ( b < 0.0) b = 0.0; else if (b > 1.0) b = 1.0; else bCheckB=false;
if ( bCheckB )
{
B = L.PointAt(b);
ClosestPointTo(B,&t);
if (t<0.0) t = 0.0; else if (t > 1.0) t = 1.0;
t = PointAt(t).DistanceTo(B);
if ( bCheckA )
{
if ( t<x ) x = t;
}
else
{
x = t;
}
}
return (x > d);
}