#include "geometry.h"
#include <math.h>
-#include "circle.h"
-#include "dimension.h"
-#include "line.h"
+#include <stdio.h>
+#include "mathconstants.h"
+// This is unused
+#if 0
Point Geometry::IntersectionOfLineAndLine(Point p1, Point p2, Point p3, Point p4)
{
// Find the intersection of the lines by formula:
return Point(px / d, py / d, 0);
}
+#endif
// Returns the parameter of a point in space to this vector. If the parameter
}
+//
+// point: The point we're rotating
+// rotationPoint: The point we're rotating around
+//
Point Geometry::RotatePointAroundPoint(Point point, Point rotationPoint, double angle)
{
- Vector v = Vector(point, rotationPoint);
+ Vector v = Vector(rotationPoint, point);
double px = (v.x * cos(angle)) - (v.y * sin(angle));
double py = (v.x * sin(angle)) + (v.y * cos(angle));
}
+int Geometry::Intersects(Object * obj1, Object * obj2, double * tp/*= 0*/, double * up/*= 0*/, double * vp/*= 0*/, double * wp/*= 0*/)
+{
+ if ((obj1->type == OTLine) && (obj2->type == OTLine))
+ return CheckLineToLineIntersection(obj1, obj2, tp, up);
+
+ return 0;
+}
+
+
/*
Intersecting line segments:
An easier way:
*/
-#if 0
-// Finds the intesection between two objects (if any)
-bool Geometry::Intersects(Object * obj1, Object * obj2, double * t, double * s)
-{
-}
-#endif
-
// Finds the intersection between two lines (if any)
-int Geometry::Intersects(Line * l1, Line * l2, double * tp/*= 0*/, double * up/*= 0*/)
+int Geometry::CheckLineToLineIntersection(Object * l1, Object * l2, double * tp, double * up)
{
- Vector r(l1->position, l1->endpoint);
- Vector s(l2->position, l2->endpoint);
- Vector v1 = l2->position - l1->position; // q - p
-// Vector v2 = l1->position - l2->position; // p - q
-//printf("l1: (%lf, %lf) (%lf, %lf), l2: (%lf, %lf) (%lf, %lf)\n", l1->position.x, l1->position.y, l1->endpoint.x, l1->endpoint.y, l2->position.x, l2->position.y, l2->endpoint.x, l2->endpoint.y);
+ Vector r(l1->p[0], l1->p[1]);
+ Vector s(l2->p[0], l2->p[1]);
+ Vector v1 = l2->p[0] - l1->p[0]; // q - p
+#if 0
+ Vector v2 = l1->p[0] - l2->p[0]; // p - q
+printf("l1: (%lf, %lf) (%lf, %lf), l2: (%lf, %lf) (%lf, %lf)\n", l1->p[0].x, l1->p[0].y, l1->p[1].x, l1->p[1].y, l2->p[0].x, l2->p[0].y, l2->p[1].x, l2->p[1].y);
+#endif
double rxs = (r.x * s.y) - (s.x * r.y);
double t, u;
{
double qpxr = (v1.x * r.y) - (r.x * v1.y);
-//printf(" --> R x S = 0! (q - p) x r = %lf\n", qpxr);
-//printf(" -->(q - p) . r = %lf, r . r = %lf\n", v1.Dot(r), r.Dot(r));
-//printf(" -->(p - q) . s = %lf, s . s = %lf\n", v2.Dot(s), s.Dot(s));
-//printf(" -->(q - p) . s = %lf, (p - q) . r = %lf\n", v1.Dot(s), v2.Dot(r));
+#if 0
+printf(" --> R x S = 0! (q - p) x r = %lf\n", qpxr);
+printf(" -->(q - p) . r = %lf, r . r = %lf\n", v1.Dot(r), r.Dot(r));
+printf(" -->(p - q) . s = %lf, s . s = %lf\n", v2.Dot(s), s.Dot(s));
+printf(" -->(q - p) . s = %lf, (p - q) . r = %lf\n", v1.Dot(s), v2.Dot(r));
+#endif
// Lines are parallel, so no intersection...
if (qpxr != 0)
return 0;
#else
// Check to see which endpoints are connected... Four possibilities:
- if (l1->position == l2->position)
+ if (l1->p[0] == l2->p[0])
t = 0, u = 0;
- else if (l1->position == l2->endpoint)
+ else if (l1->p[0] == l2->p[1])
t = 0, u = 1.0;
- else if (l1->endpoint == l2->position)
+ else if (l1->p[1] == l2->p[0])
t = 1.0, u = 0;
- else if (l1->endpoint == l2->endpoint)
+ else if (l1->p[1] == l2->p[1])
t = 1.0, u = 1.0;
else
return 0;
}
+#if 0
// Finds the intersection between two lines (if any)
int Geometry::Intersects(Line * l1, Dimension * d1, double * tp/*= 0*/, double * up/*= 0*/)
{
}
-// Finds the intesection(s) between a line and a circle (if any)
+// Finds the intersection(s) between a line and a circle (if any)
int Geometry::Intersects(Line * l, Circle * c, double * tp/*= 0*/, double * up/*= 0*/, double * vp/*= 0*/, double * wp/*= 0*/)
{
#if 0
// Now we have to check for intersection points.
// Tangent case: (needs to return something)
if ((distance == c->radius) && (t >= 0.0) && (t <= 1.0))
+ {
+ // Need to set tp & up to something... !!! FIX !!!
+ if (tp)
+ *tp = t;
+
+ if (up)
+ *up = Vector(c->position, p).Angle();
+
return 1;
+ }
// The line intersects the circle in two points (possibly). Use Pythagorus
// to find them for testing.
}
+// Finds the intersection(s) between a circle and a circle (if any)
+// There can be 0, 1, or 2 intersections.
+// Returns the angles of the points of intersection in tp thru wp, with the
+// angles returned as c1, c2, c1, c2 (if applicable--in the 1 intersection case,
+// only the first two angles are returned: c1, c2).
+int Geometry::Intersects(Circle * c1, Circle * c2, double * tp/*= 0*/, double * up/*= 0*/, double * vp/*= 0*/, double * wp/*= 0*/, Point * p1/*= 0*/, Point * p2/*= 0*/)
+{
+ // Get the distance between centers. If the distance plus the radius of the
+ // smaller circle is less than the radius of the larger circle, there is no
+ // intersection. If the distance is greater than the sum of the radii,
+ // there is no intersection. If the distance is equal to the sum of the
+ // radii, they are tangent and intersect at one point. Otherwise, they
+ // intersect at two points.
+ Vector centerLine(c1->position, c2->position);
+ double d = centerLine.Magnitude();
+//printf("Circle #1: pos=<%lf, %lf>, r=%lf\n", c1->position.x, c1->position.y, c1->radius);
+//printf("Circle #2: pos=<%lf, %lf>, r=%lf\n", c2->position.x, c2->position.y, c2->radius);
+//printf("Distance between #1 & #2: %lf\n", d);
+
+ // Check to see if we actually have an intersection, and return failure if not
+ if ((fabs(c1->radius - c2->radius) > d) || ((c1->radius + c2->radius) < d))
+ return 0;
+
+ // There are *two* tangent cases!
+ if (((c1->radius + c2->radius) == d) || (fabs(c1->radius - c2->radius) == d))
+ {
+ // Need to return something in tp & up!! !!! FIX !!! [DONE]
+ if (tp)
+ *tp = centerLine.Angle();
+
+ if (up)
+ *up = centerLine.Angle() + PI;
+
+ return 1;
+ }
+
+ // Find the distance from the center of c1 to the perpendicular chord
+ // (which contains the points of intersection)
+ double x = ((d * d) - (c2->radius * c2->radius) + (c1->radius * c1->radius))
+ / (2.0 * d);
+ // Find the the length of the perpendicular chord
+// Not needed...!
+ double a = sqrt((-d + c2->radius - c1->radius) * (-d - c2->radius + c1->radius) * (-d + c2->radius + c1->radius) * (d + c2->radius + c1->radius)) / d;
+
+ // Now, you can use pythagorus to find the length of the hypotenuse, but we
+ // already know that length, it's the radius! :-P
+ // What's needed is the angle of the center line and the radial line. Since
+ // there's two intersection points, there's also four angles (two for each
+ // circle)!
+ // We can use the arccos to find the angle using just the radius and the
+ // distance to the perpendicular chord...!
+ double angleC1 = acos(x / c1->radius);
+ double angleC2 = acos((d - x) / c2->radius);
+
+ if (tp)
+ *tp = centerLine.Angle() - angleC1;
+
+ if (up)
+ *up = (centerLine.Angle() + PI) - angleC2;
+
+ if (vp)
+ *vp = centerLine.Angle() + angleC1;
+
+ if (wp)
+ *wp = (centerLine.Angle() + PI) + angleC2;
+
+ if (p1)
+ *p1 = c1->position + (centerLine.Unit() * x) + (Vector::Normal(Vector(), centerLine) * (a / 2.0));
+
+ if (p2)
+ *p2 = c1->position + (centerLine.Unit() * x) - (Vector::Normal(Vector(), centerLine) * (a / 2.0));
+
+ return 2;
+}
+#endif
+
+// should we just do common trig solves, like AAS, ASA, SAS, SSA?
+// Law of Cosines:
+// c^2 = a^2 + b^2 -2ab*cos(C)
+// Solving for C:
+// cos(C) = (c^2 - a^2 - b^2) / -2ab = (a^2 + b^2 - c^2) / 2ab
+// Law of Sines:
+// a / sin A = b / sin B = c / sin C
+
+// Solve the angles of the triangle given the sides. Angles returned are
+// opposite of the given sides (so a1 consists of sides s2 & s3, and so on).
+void Geometry::FindAnglesForSides(double s1, double s2, double s3, double * a1, double * a2, double * a3)
+{
+ // Use law of cosines to find 1st angle
+ double cosine1 = ((s2 * s2) + (s3 * s3) - (s1 * s1)) / (2.0 * s2 * s3);
+
+ // Check for a valid triangle
+ if ((cosine1 < -1.0) || (cosine1 > 1.0))
+ return;
+
+ double angle1 = acos(cosine1);
+
+ // Use law of sines to find 2nd & 3rd angles
+// sin A / a = sin B / b
+// sin B = (sin A / a) * b
+// B = arcsin( sin A * (b / a))
+// ??? ==> B = A * arcsin(b / a)
+/*
+Well, look here:
+sin B = sin A * (b / a)
+sin B / sin A = b / a
+arcsin( sin B / sin A ) = arcsin( b / a )
+
+hmm... dunno...
+*/
+
+ double angle2 = asin(s2 * (sin(angle1) / s1));
+ double angle3 = asin(s3 * (sin(angle1) / s1));
+
+ if (a1)
+ *a1 = angle1;
+
+ if (a2)
+ *a2 = angle2;
+
+ if (a3)
+ *a3 = angle3;
+}
+
+
+Point Geometry::GetPointForParameter(Object * obj, double t)
+{
+ if (obj->type == OTLine)
+ {
+ // Translate line vector to the origin, then add the scaled vector to
+ // initial point of the line.
+ Vector v = obj->p[1] - obj->p[0];
+ return obj->p[0] + (v * t);
+ }
+
+ return Point(0, 0);
+}
+
projects / architektonas / blobdiff