ON_BOOL32 ON_ArcCurve::SetEndPoint(ON_3dPoint end_point)
{
if (IsCircle())
return false;
ON_BOOL32 rc = false;
if ( m_dim == 3 || end_point.z == 0.0 )
{
ON_3dPoint P;
ON_3dVector T;
double t = Domain()[0];
Ev1Der( t, P, T );
ON_Arc a;
rc = a.Create( P, T, end_point );
if ( rc )
{
m_arc = a;
}
else {
ON_3dPoint start_point = PointAt(Domain()[0]);
if (end_point.DistanceTo(start_point) < ON_ZERO_TOLERANCE*m_arc.Radius()){
//make arc into circle
m_arc.plane.xaxis = start_point - m_arc.Center();
m_arc.plane.xaxis.Unitize();
m_arc.plane.yaxis = ON_CrossProduct(m_arc.Normal(), m_arc.plane.xaxis);
m_arc.plane.yaxis.Unitize();
m_arc.SetAngleRadians(2.0*ON_PI);
rc = true;
}
}
}
return rc;
}
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;
}
/* approximates a bezier curve with a set of circular arcs by dividing where
* the bezier's deviation from its approximating biarc is at a maximum, then
* recursively calling on the subsections until it is approximated to
* tolerance by the biarc
*/
HIDDEN void
approx_bezier(const ON_BezierCurve& bezier, const ON_Arc& biarc, const struct bn_tol *tol, std::vector<ON_Arc>& approx)
{
fastf_t t = 0.0, step = 0.0;
fastf_t crv = 0.0, err = 0.0, max_t = 0.0, max_err = 0.0;
ON_3dPoint test;
ON_3dVector d1, d2;
// walk the bezier curve at interval given by step
for (t = 0; t <= 1.0; t += step) {
bezier.Ev2Der(t, test, d1, d2);
err = fabs((test - biarc.Center()).Length() - biarc.Radius());
// find the maximum point of deviation
if (err > max_err) {
max_t = t;
max_err = err;
}
crv = CURVATURE(d1, d2);
// step size decreases as |crv| -> 1
step = GETSTEPSIZE(1.0 - fabs(crv));
}
if (max_err + VDIVIDE_TOL < tol->dist) {
// max deviation is less than the given tolerance, add the biarc approximation
approx.push_back(biarc);
} else {
ON_BezierCurve head, tail;
// split bezier at point of maximum deviation and recurse on the new subsections
bezier.Split(max_t, head, tail);
approx_bezier(head, make_biarc(head), tol, approx);
approx_bezier(tail, make_biarc(tail), tol, approx);
}
}
/* approximates a bezier curve with a set of circular arcs.
* returns approximation in carcs
*/
HIDDEN void
bezier_to_carcs(const ON_BezierCurve& bezier, const struct bn_tol *tol, std::vector<ON_Arc>& carcs)
{
bool skip_while = true, curvature_changed = false;
fastf_t inflection_pt, biarc_angle;
ON_Arc biarc;
ON_BezierCurve current, next;
std::vector<ON_BezierCurve> rest;
// find inflection point, if it exists
if (bezier_inflection(bezier, inflection_pt)) {
curvature_changed = true;
bezier.Split(inflection_pt, current, next);
rest.push_back(next);
} else {
current = bezier;
}
while (skip_while || !rest.empty()) {
if (skip_while) skip_while = false;
biarc = make_biarc(current);
if ((biarc_angle = biarc.AngleRadians()) <= M_PI_2) {
// approximate the current bezier segment and add its biarc
// approximation to carcs
approx_bezier(current, biarc, tol, carcs);
} else if (biarc_angle <= M_PI) {
// divide the current bezier segment in half
current.Split(0.5, current, next);
// approximate first bezier segment
approx_bezier(current, biarc, tol, carcs);
// approximate second bezier segment
approx_bezier(next, biarc, tol, carcs);
} else {
fastf_t t = 1.0;
ON_Arc test_biarc;
ON_BezierCurve test_bezier;
// divide the current bezier such that the first curve segment would
// have an approximating biarc segment <=90 degrees
do {
t *= 0.5;
current.Split(t, test_bezier, next);
test_biarc = make_biarc(test_bezier);
} while(test_biarc.AngleRadians() > M_PI_2);
approx_bezier(test_bezier, test_biarc, tol, carcs);
current = next;
skip_while = true;
continue;
}
if (curvature_changed) {
curvature_changed = false;
current = rest.back();
rest.pop_back();
// continue even if we just popped the last element
skip_while = true;
}
}
}
ON_RevSurface* ON_Sphere::RevSurfaceForm(
bool bArcLengthParameterization,
ON_RevSurface* srf
) const
{
if ( srf )
srf->Destroy();
ON_RevSurface* pRevSurface = NULL;
if ( IsValid() )
{
ON_Arc arc;
arc.plane.origin = plane.origin;
arc.plane.xaxis = -plane.zaxis;
arc.plane.yaxis = plane.xaxis;
arc.plane.zaxis = -plane.yaxis;
arc.plane.UpdateEquation();
arc.radius = radius;
arc.SetAngleRadians(ON_PI);
ON_ArcCurve* arc_curve = new ON_ArcCurve( arc, -0.5*ON_PI, 0.5*ON_PI );
if ( srf )
pRevSurface = srf;
else
pRevSurface = new ON_RevSurface();
pRevSurface->m_angle.Set(0.0,2.0*ON_PI);
pRevSurface->m_t = pRevSurface->m_angle;
pRevSurface->m_curve = arc_curve;
pRevSurface->m_axis.from = plane.origin;
pRevSurface->m_axis.to = plane.origin + plane.zaxis;
pRevSurface->m_bTransposed = false;
pRevSurface->m_bbox.m_min = plane.origin;
pRevSurface->m_bbox.m_min.x -= radius;
pRevSurface->m_bbox.m_min.y -= radius;
pRevSurface->m_bbox.m_min.z -= radius;
pRevSurface->m_bbox.m_max = plane.origin;
pRevSurface->m_bbox.m_max.x += radius;
pRevSurface->m_bbox.m_max.y += radius;
pRevSurface->m_bbox.m_max.z += radius;
if ( bArcLengthParameterization )
{
double r = fabs(radius);
if ( !(r > ON_SQRT_EPSILON) )
r = 1.0;
r *= ON_PI;
pRevSurface->SetDomain(0,0.0,2.0*r);
pRevSurface->SetDomain(1,-0.5*r,0.5*r);
}
}
return pRevSurface;
}
ON_RevSurface* ON_Sphere::RevSurfaceForm( ON_RevSurface* srf ) const
{
if ( srf )
srf->Destroy();
ON_RevSurface* pRevSurface = NULL;
if ( IsValid() )
{
ON_Arc arc;
arc.plane.origin = plane.origin;
arc.plane.xaxis = -plane.zaxis;
arc.plane.yaxis = plane.xaxis;
arc.plane.zaxis = -plane.yaxis;
arc.plane.UpdateEquation();
arc.radius = radius;
arc.SetAngleRadians(ON_PI);
ON_ArcCurve* arc_curve = new ON_ArcCurve( arc, -0.5*ON_PI, 0.5*ON_PI );
if ( srf )
pRevSurface = srf;
else
pRevSurface = new ON_RevSurface();
pRevSurface->m_angle.Set(0.0,2.0*ON_PI);
pRevSurface->m_t = pRevSurface->m_angle;
pRevSurface->m_curve = arc_curve;
pRevSurface->m_axis.from = plane.origin;
pRevSurface->m_axis.to = plane.origin + plane.zaxis;
pRevSurface->m_bTransposed = false;
pRevSurface->m_bbox.m_min = plane.origin;
pRevSurface->m_bbox.m_min.x -= radius;
pRevSurface->m_bbox.m_min.y -= radius;
pRevSurface->m_bbox.m_min.z -= radius;
pRevSurface->m_bbox.m_max = plane.origin;
pRevSurface->m_bbox.m_max.x += radius;
pRevSurface->m_bbox.m_max.y += radius;
pRevSurface->m_bbox.m_max.z += radius;
}
return pRevSurface;
}
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;
}
static ON_BOOL32 NurbsCurveArc ( const ON_Arc& arc, int dim, ON_NurbsCurve& nurb )
{
if ( !arc.IsValid() )
return false;
// makes a quadratic nurbs arc
const ON_3dPoint center = arc.Center();
double angle = arc.AngleRadians();
ON_Interval dom = arc.DomainRadians();
const double angle0 = dom[0];
const double angle1 = dom[1];
ON_3dPoint start_point = arc.StartPoint();
//ON_3dPoint mid_point = arc.PointAt(angle0 + 0.5*angle);
ON_3dPoint end_point = arc.IsCircle() ? start_point : arc.EndPoint();
ON_4dPoint CV[9];
double knot[10];
double a, b, c, w, winv;
double *cv;
int j, span_count, cv_count;
a = (0.5 + ON_SQRT_EPSILON)*ON_PI;
if (angle <= a)
span_count = 1;
else if (angle <= 2.0*a)
span_count = 2;
else if (angle <= 3.0*a)
span_count = 4; // TODO - make a 3 span case
else
span_count = 4;
cv_count = 2*span_count + 1;
switch(span_count) {
case 1:
CV[0] = start_point;
CV[1] = arc.PointAt(angle0 + 0.50*angle);
CV[2] = end_point;
break;
case 2:
CV[0] = start_point;
CV[1] = arc.PointAt(angle0 + 0.25*angle);
CV[2] = arc.PointAt(angle0 + 0.50*angle);
CV[3] = arc.PointAt(angle0 + 0.75*angle);
CV[4] = end_point;
angle *= 0.5;
break;
default: // 4 spans
CV[0] = start_point;
CV[1] = arc.PointAt(angle0 + 0.125*angle);
CV[2] = arc.PointAt(angle0 + 0.250*angle);
CV[3] = arc.PointAt(angle0 + 0.375*angle);
CV[4] = arc.PointAt(angle0 + 0.500*angle);
CV[5] = arc.PointAt(angle0 + 0.625*angle);
CV[6] = arc.PointAt(angle0 + 0.750*angle);
CV[7] = arc.PointAt(angle0 + 0.875*angle);
CV[8] = end_point;
angle *= 0.25;
break;
}
a = cos(0.5*angle);
b = a - 1.0;
//c = (radius > 0.0) ? radius*angle : angle;
c = angle;
span_count *= 2;
knot[0] = knot[1] = angle0; //0.0;
for (j = 1; j < span_count; j += 2) {
CV[j].x += b * center.x;
CV[j].y += b * center.y;
CV[j].z += b * center.z;
CV[j].w = a;
CV[j+1].w = 1.0;
knot[j+1] = knot[j+2] = knot[j-1] + c;
}
knot[cv_count-1] = knot[cv_count] = angle1;
for ( j = 1; j < span_count; j += 2 ) {
w = CV[j].w;
winv = 1.0/w;
a = CV[j].x*winv;
b = ArcDeFuzz(a);
if ( a != b ) {
CV[j].x = b*w;
}
a = CV[j].y*winv;
b = ArcDeFuzz(a);
if ( a != b ) {
CV[j].y = b*w;
}
a = CV[j].z*winv;
b = ArcDeFuzz(a);
if ( a != b ) {
CV[j].z = b*w;
}
}
nurb.m_dim = (dim==2) ? 2 : 3;
nurb.m_is_rat = 1;
nurb.m_order = 3;
nurb.m_cv_count = cv_count;
nurb.m_cv_stride = (dim==2 ? 3 : 4);
nurb.ReserveCVCapacity( nurb.m_cv_stride*cv_count );
nurb.ReserveKnotCapacity( cv_count+1 );
for ( j = 0; j < cv_count; j++ ) {
cv = nurb.CV(j);
cv[0] = CV[j].x;
cv[1] = CV[j].y;
if ( dim == 2 ) {
cv[2] = CV[j].w;
}
else {
cv[2] = CV[j].z;
cv[3] = CV[j].w;
}
nurb.m_knot[j] = knot[j];
}
nurb.m_knot[cv_count] = knot[cv_count];
return true;
}