double Span::Parameter(const Point& p)const
{
double t;
if(m_v.m_type == 0) {
Point v0 = p - m_p;
Point vs = m_v.m_p - m_p;
double length = vs.length();
vs.normalize();
t = vs * v0;
t = t / length;
}
else
{
// true if p lies on arc span sp (p must be on circle of span)
Point vs = ~(m_p - m_v.m_c);
Point v = ~(p - m_v.m_c);
vs.normalize();
v.normalize();
if(m_v.m_type == -1){
vs = -vs;
v = -v;
}
double ang = ::IncludedAngle(vs, v, m_v.m_type);
double angle = IncludedAngle();
t = ang / angle;
}
return t;
}
double Span::Length()const
{
if(m_v.m_type) {
double radius = m_p.dist(m_v.m_c);
return fabs(IncludedAngle()) * radius;
}
return m_p.dist(m_v.m_p);
}
double Span::GetArea()const
{
if(m_v.m_type)
{
double angle = IncludedAngle();
double radius = m_p.dist(m_v.m_c);
return ( 0.5 * ((m_v.m_c.x - m_p.x) * (m_v.m_c.y + m_p.y) - (m_v.m_c.x - m_v.m_p.x) * (m_v.m_c.y + m_v.m_p.y) - angle * radius * radius));
}
return 0.5 * (m_v.m_p.x - m_p.x) * (m_p.y + m_v.m_p.y);
}
Point CArc::MidParam(double param)const {
/// returns a point which is 0-1 along arc
if(fabs(param) < 0.00000000000001)return m_s;
if(fabs(param - 1.0) < 0.00000000000001)return m_e;
Point p;
Point v = m_s - m_c;
v.Rotate(param * IncludedAngle());
p = v + m_c;
return p;
}
Point Span::MidParam(double param)const {
/// returns a point which is 0-1 along span
if(fabs(param) < 0.00000000000001)return m_p;
if(fabs(param - 1.0) < 0.00000000000001)return m_v.m_p;
Point p;
if(m_v.m_type == 0) {
Point vs = m_v.m_p - m_p;
p = vs * param + m_p;
}
else {
Point v = m_p - m_v.m_c;
v.Rotate(param * IncludedAngle());
p = v + m_v.m_c;
}
return p;
}
bool Span::OnSpan(const Point& p, double* t)const {
// FAST OnSpan test - assumes that p lies ON the unbounded span
#if _DEBUG
if(this->returnSpanProperties == false) {
FAILURE(L"OnSpan - properties no set, incorrect calling code");
}
#endif
#if 0
if(NullSpan) {
*t = 0.0;
return (p == p0);
}
if(p == p0) {
*t = 0.0;
return true;
}
if(p == p1) {
*t = 1.0;
return true;
}
#endif
bool ret;
// if(p == this->p0 || p == this->p1) return true;
if(dir == LINEAR) {
#if 1
#if _DEBUG
// check p is on line
CLine cl(*this);
double d = fabs(cl.Dist(p));
if( d > geoff_geometry::TOLERANCE) {
FAILURE(L"OnSpan - point not on linear span, incorrect calling code");
}
#endif
#endif
Vector2d v0(p0, p);
*t = vs * v0;
// ret = (*t > - geoff_geometry::TOLERANCE && *t < length + geoff_geometry::TOLERANCE);
*t = *t / length;
ret = (*t >= 0 && *t <= 1.0 );
}
else {
// true if p lies on arc span sp (p must be on circle of span)
#if 1
#if _DEBUG
// check that p lies on the arc
double d = p.Dist(pc);
if(FNE(d, radius, geoff_geometry::TOLERANCE)) {
FAILURE(L"OnSpan - point not on circular span, incorrect calling code");
}
#endif
#endif
#if 0 // alt method (faster, but doesn't provide t)
Vector2d v0(p0, p);
Vector2d v1(p0, p1);
// check angle to point from start
double cp;
ret = ((cp = (dir * (v0 ^ v1))) > 0);
*t = 0.0;// incorrect !!!
#else
Vector2d v = ~Vector2d(pc, p);
v.normalise();
if(dir == CW) v = -v;
double ang = IncludedAngle(vs, v, dir);
*t = ang / angle;
ret = (*t >= 0 && *t <= 1.0);
#endif
}
return ret;
}
