public void CircleProjectionToPlaneTest()
{
Vector3d v1 = new Vector3d(3, 5, 1);
Circle3d c = new Circle3d(new Point3d(5, 6, 1), 5, v1);
Plane3d s = new Plane3d(5, 2, 3, -3);
Point3d p = c.ParametricForm(0.5).ProjectionTo(s);
Assert.IsTrue(p.BelongsTo(c.ProjectionTo(s)));
p = c.ParametricForm(0.725).ProjectionTo(s);
Assert.IsTrue(p.BelongsTo(c.ProjectionTo(s)));
p = c.ParametricForm(2.7122).ProjectionTo(s);
Assert.IsTrue(p.BelongsTo(c.ProjectionTo(s)));
}
public void EllipseProjectionToPlaneTest()
{
Vector3d v1 = new Vector3d(3, 0, 1);
Vector3d v2 = 3 * v1.OrthogonalVector;
Ellipse e = new Ellipse(new Point3d(5, 6, 1), v1, v2);
Plane3d s = new Plane3d(5, 2, 3, -3);
Point3d p = e.ParametricForm(0.5).ProjectionTo(s);
Assert.IsTrue(p.BelongsTo(e.ProjectionTo(s)));
p = e.ParametricForm(0.725).ProjectionTo(s);
Assert.IsTrue(p.BelongsTo(e.ProjectionTo(s)));
p = e.ParametricForm(2.7122).ProjectionTo(s);
Assert.IsTrue(p.BelongsTo(e.ProjectionTo(s)));
}
public void EllipsoidProjectionToLineTest_2()
{
Point3d p = new Point3d(0, 0, 0);
Vector3d v1 = new Vector3d(4, 0, 0);
Vector3d v2 = new Vector3d(0, 6, 0);
Vector3d v3 = new Vector3d(0, 0, 9);
Ellipsoid e = new Ellipsoid(p, v1, v2, v3);
p = new Point3d(1, 1, 1);
v1 = new Vector3d(1, 1, 3);
Line3d l = new Line3d(p, v1);
Segment3d s = e.ProjectionTo(l);
// Construct plane orthogonal to line and passing through segment end point
// And check if it is touching ellipsoid
Plane3d pl1 = new Plane3d(s.P1, v1);
object obj = e.IntersectionWith(pl1);
if (obj.GetType() == typeof(Point3d))
{
p = (Point3d)obj;
if (p.BelongsTo(e))
{
Assert.IsTrue(true);
}
else
{
Assert.Fail();
}
}
else
{
Assert.Fail();
}
}
public void PointInAlignedBoxTest()
{
Point3d p = new Point3d(1, 1, 1);
Box3d box = new Box3d(p, 8, 6, 10);
p = new Point3d(2, 2, 2); // Point inside
Assert.IsTrue(p.BelongsTo(box));
Assert.IsTrue(p.IsInside(box));
Assert.IsFalse(p.IsOutside(box));
Assert.IsFalse(p.IsOnBoundary(box));
p = new Point3d(2, 4, 2); // Point on side
Assert.IsTrue(p.BelongsTo(box));
Assert.IsFalse(p.IsInside(box));
Assert.IsFalse(p.IsOutside(box));
Assert.IsTrue(p.IsOnBoundary(box));
p = new Point3d(5, 4, 6); // Point in corner
Assert.IsTrue(p.BelongsTo(box));
Assert.IsFalse(p.IsInside(box));
Assert.IsFalse(p.IsOutside(box));
Assert.IsTrue(p.IsOnBoundary(box));
p = new Point3d(5, -5, 6); // Point outside
Assert.IsFalse(p.BelongsTo(box));
Assert.IsFalse(p.IsInside(box));
Assert.IsTrue(p.IsOutside(box));
Assert.IsFalse(p.IsOnBoundary(box));
}
public void PointBelongsToPlaneTest()
{
Plane3d s1 = new Plane3d(-1, 2, -2, 9);
Point3d p1 = s1.Point;
Assert.IsTrue(p1.BelongsTo(s1));
s1 = new Plane3d(new Point3d(0, 0, 10), new Vector3d(0, 0, 1));
p1 = new Point3d(0, 0, 10);
Assert.IsTrue(p1.BelongsTo(s1));
double tol = GeometRi3D.Tolerance;
bool mode = GeometRi3D.UseAbsoluteTolerance;
GeometRi3D.Tolerance = 0.01;
GeometRi3D.UseAbsoluteTolerance = false;
s1 = new Plane3d(new Point3d(0, 0, 10), new Vector3d(0, 0, 100));
p1 = new Point3d(0, 0, 10.05);
Assert.IsTrue(p1.BelongsTo(s1));
p1 = new Point3d(0, 0, 10.15);
Assert.IsFalse(p1.BelongsTo(s1));
// Resore initial state
GeometRi3D.UseAbsoluteTolerance = mode;
GeometRi3D.Tolerance = tol;
}
public void PointInsideRelativeTest()
{
Point3d a = new Point3d(0, 0, 0);
Point3d b = new Point3d(15, 0, 0);
Point3d p = new Point3d(0, 15, 0);
Triangle s = new Triangle(a, b, p);
double tol = GeometRi3D.Tolerance;
bool mode = GeometRi3D.UseAbsoluteTolerance;
GeometRi3D.Tolerance = 0.01;
GeometRi3D.UseAbsoluteTolerance = false;
p = new Point3d(1, 1, 0.1); // Point inside
Assert.IsTrue(p.BelongsTo(s));
Assert.IsTrue(p.IsInside(s));
Assert.IsFalse(p.IsOutside(s));
Assert.IsFalse(p.IsOnBoundary(s));
p = new Point3d(0.2, 5, 0.0); // Point inside
Assert.IsTrue(p.BelongsTo(s));
Assert.IsTrue(p.IsInside(s));
Assert.IsFalse(p.IsOutside(s));
Assert.IsFalse(p.IsOnBoundary(s));
// Resore initial state
GeometRi3D.UseAbsoluteTolerance = mode;
GeometRi3D.Tolerance = tol;
}
public void PointInTriangleTest2()
{
Point3d p1 = new Point3d(0, 0, 0);
Point3d p2 = new Point3d(6, 0, 0);
Point3d p3 = new Point3d(0, 6, 0);
Triangle t = new Triangle(p1, p2, p3);
Point3d p = new Point3d(4, 4, 0);
Assert.IsFalse(p.BelongsTo(t));
p = new Point3d(6, 0.5, 0);
Assert.IsFalse(p.BelongsTo(t));
p = new Point3d(5, -0.5, 0);
Assert.IsFalse(p.BelongsTo(t));
p = new Point3d(2, 5, 0);
Assert.IsFalse(p.BelongsTo(t));
p = new Point3d(2, 2, 0.1);
Assert.IsFalse(p.BelongsTo(t));
p = new Point3d(2, 2, 0);
Assert.IsTrue(p.BelongsTo(t));
p = new Point3d(5, 1, 0);
Assert.IsTrue(p.BelongsTo(t));
p = new Point3d(0, 1, 0);
Assert.IsTrue(p.BelongsTo(t));
p = new Point3d(2, 0, 0);
Assert.IsTrue(p.BelongsTo(t));
}
public void PointInSegmentTest()
{
Point3d p = new Point3d(0, 0, 0);
Segment3d s = new Segment3d(p, new Point3d(10, 0, 0));
p = new Point3d(5, 0, 0); // Point inside
Assert.IsTrue(p.BelongsTo(s));
Assert.IsTrue(p.IsInside(s));
Assert.IsFalse(p.IsOutside(s));
Assert.IsFalse(p.IsOnBoundary(s));
p = new Point3d(10, 0, 0); // Point on boundary
Assert.IsTrue(p.BelongsTo(s));
Assert.IsFalse(p.IsInside(s));
Assert.IsFalse(p.IsOutside(s));
Assert.IsTrue(p.IsOnBoundary(s));
p = new Point3d(1, 3, 0); // Point outside
Assert.IsFalse(p.BelongsTo(s));
Assert.IsFalse(p.IsInside(s));
Assert.IsTrue(p.IsOutside(s));
Assert.IsFalse(p.IsOnBoundary(s));
p = new Point3d(11, 0, 0); // Point outside
Assert.IsFalse(p.BelongsTo(s));
Assert.IsFalse(p.IsInside(s));
Assert.IsTrue(p.IsOutside(s));
Assert.IsFalse(p.IsOnBoundary(s));
}
public void PointInSphereRelativeTest()
{
Point3d p = new Point3d(1, 1, 1);
Sphere s = new Sphere(p, 5);
double tol = GeometRi3D.Tolerance;
bool mode = GeometRi3D.UseAbsoluteTolerance;
GeometRi3D.Tolerance = 0.01;
GeometRi3D.UseAbsoluteTolerance = false;
p = new Point3d(1, 5.9, 1); // Point inside
Assert.IsTrue(p.BelongsTo(s));
Assert.IsTrue(p.IsInside(s));
Assert.IsFalse(p.IsOutside(s));
Assert.IsFalse(p.IsOnBoundary(s));
p = new Point3d(1, 6.04, 1); // Point on surface
Assert.IsTrue(p.BelongsTo(s));
Assert.IsFalse(p.IsInside(s));
Assert.IsFalse(p.IsOutside(s));
Assert.IsTrue(p.IsOnBoundary(s));
p = new Point3d(1, 6.06, 1); // Point outside
Assert.IsFalse(p.BelongsTo(s));
Assert.IsFalse(p.IsInside(s));
Assert.IsTrue(p.IsOutside(s));
Assert.IsFalse(p.IsOnBoundary(s));
// Resore initial state
GeometRi3D.UseAbsoluteTolerance = mode;
GeometRi3D.Tolerance = tol;
}
public void PointInEllipseTest()
{
Point3d p = new Point3d(1, 1, 0);
Ellipse s = new Ellipse(p, new Vector3d(10, 0, 0), new Vector3d(0, 5, 0));
p = new Point3d(2, 2, 0); // Point inside
Assert.IsTrue(p.BelongsTo(s));
Assert.IsTrue(p.IsInside(s));
Assert.IsFalse(p.IsOutside(s));
Assert.IsFalse(p.IsOnBoundary(s));
p = new Point3d(1, 6, 0); // Point on boundary
Assert.IsTrue(p.BelongsTo(s));
Assert.IsFalse(p.IsInside(s));
Assert.IsFalse(p.IsOutside(s));
Assert.IsTrue(p.IsOnBoundary(s));
p = new Point3d(1, 6.005, 0); // Point outside
Assert.IsFalse(p.BelongsTo(s));
Assert.IsFalse(p.IsInside(s));
Assert.IsTrue(p.IsOutside(s));
Assert.IsFalse(p.IsOnBoundary(s));
p = new Point3d(1, 2, 0.01); // Point outside
Assert.IsFalse(p.BelongsTo(s));
Assert.IsFalse(p.IsInside(s));
Assert.IsTrue(p.IsOutside(s));
Assert.IsFalse(p.IsOnBoundary(s));
}
public void PointInCircleTest()
{
Point3d p = new Point3d(1, 1, 0);
Circle3d s = new Circle3d(p, 5, new Vector3d(0, 0, 1));
p = new Point3d(2, 2, 0); // Point inside
Assert.IsTrue(p.BelongsTo(s));
Assert.IsTrue(p.IsInside(s));
Assert.IsFalse(p.IsOutside(s));
Assert.IsFalse(p.IsOnBoundary(s));
p = new Point3d(1, 6, 0); // Point on boundary
Assert.IsTrue(p.BelongsTo(s));
Assert.IsFalse(p.IsInside(s));
Assert.IsFalse(p.IsOutside(s));
Assert.IsTrue(p.IsOnBoundary(s));
p = new Point3d(1, 6.005, 0); // Point outside
Assert.IsFalse(p.BelongsTo(s));
Assert.IsFalse(p.IsInside(s));
Assert.IsTrue(p.IsOutside(s));
Assert.IsFalse(p.IsOnBoundary(s));
p = new Point3d(1, 2, 0.01); // Point outside
Assert.IsFalse(p.BelongsTo(s));
Assert.IsFalse(p.IsInside(s));
Assert.IsTrue(p.IsOutside(s));
Assert.IsFalse(p.IsOnBoundary(s));
}
public void PointInTriangleTest()
{
Point3d a = new Point3d(0, 0, 0);
Point3d b = new Point3d(15, 0, 0);
Point3d p = new Point3d(0, 15, 0);
Triangle s = new Triangle(a, b, p);
p = new Point3d(1, 1, 0); // Point inside
Assert.IsTrue(p.BelongsTo(s));
Assert.IsTrue(p.IsInside(s));
Assert.IsFalse(p.IsOutside(s));
Assert.IsFalse(p.IsOnBoundary(s));
p = new Point3d(10, 0, 0); // Point on boundary
Assert.IsTrue(p.BelongsTo(s));
Assert.IsFalse(p.IsInside(s));
Assert.IsFalse(p.IsOutside(s));
Assert.IsTrue(p.IsOnBoundary(s));
p = new Point3d(1, 3, 1); // Point outside
Assert.IsFalse(p.BelongsTo(s));
Assert.IsFalse(p.IsInside(s));
Assert.IsTrue(p.IsOutside(s));
Assert.IsFalse(p.IsOnBoundary(s));
p = new Point3d(16, 0, 0); // Point outside
Assert.IsFalse(p.BelongsTo(s));
Assert.IsFalse(p.IsInside(s));
Assert.IsTrue(p.IsOutside(s));
Assert.IsFalse(p.IsOnBoundary(s));
}
public void PointBelongsToLineTest()
{
Point3d p1 = new Point3d(1, -5, -1);
Vector3d v1 = new Vector3d(-2, 3, 4);
Line3d l1 = new Line3d(p1, v1);
Point3d p2 = p1.Translate(3 * v1);
Assert.IsTrue(p2.BelongsTo(l1));
}
public void LineProjectionToPlaneTest()
{
Point3d p1 = new Point3d(1, -5, -1);
Vector3d v1 = new Vector3d(-2, 3, 4);
Line3d l1 = new Line3d(p1, v1);
Plane3d s1 = new Plane3d(-2, 2, 3, -29);
Point3d p2 = (Point3d)l1.IntersectionWith(s1);
Line3d l2 = (Line3d)l1.ProjectionTo(s1);
Assert.IsTrue(p2.BelongsTo(l2));
}
public void PointBelongsToRayTest()
{
Point3d p = new Point3d(0, 0, 0);
Ray3d r = new Ray3d(new Point3d(1, 1, 0), new Vector3d(1, 0, 0));
Assert.IsFalse(p.BelongsTo(r));
p = new Point3d(1, 1, 0);
Assert.IsTrue(p.BelongsTo(r));
p = new Point3d(3, 1, 0);
Assert.IsTrue(p.BelongsTo(r));
}
public void PointBelongsToSegmentTest()
{
Point3d p = new Point3d(0, 0, 0);
Segment3d s = new Segment3d(new Point3d(1, 1, 0), new Point3d(3, 3, 0));
Assert.IsFalse(p.BelongsTo(s));
p = new Point3d(1, 1, 0);
Assert.IsTrue(p.BelongsTo(s));
p = new Point3d(2, 2, 0);
Assert.IsTrue(p.BelongsTo(s));
p = new Point3d(3, 3, 0);
Assert.IsTrue(p.BelongsTo(s));
}
public void PointInEllipseRelativeTest()
{
Point3d p = new Point3d(1, 1, 0);
Ellipse s = new Ellipse(p, new Vector3d(10, 0, 0), new Vector3d(0, 5, 0));
double tol = GeometRi3D.Tolerance;
bool mode = GeometRi3D.UseAbsoluteTolerance;
GeometRi3D.Tolerance = 0.01;
GeometRi3D.UseAbsoluteTolerance = false;
p = new Point3d(2, 2, 0.1); // Point inside
Assert.IsTrue(p.BelongsTo(s));
Assert.IsTrue(p.IsInside(s));
Assert.IsFalse(p.IsOutside(s));
Assert.IsFalse(p.IsOnBoundary(s));
p = new Point3d(1, 6, 0); // Point on boundary
Assert.IsTrue(p.BelongsTo(s));
Assert.IsFalse(p.IsInside(s));
Assert.IsFalse(p.IsOutside(s));
Assert.IsTrue(p.IsOnBoundary(s));
p = new Point3d(1, 6.2, 0); // Point outside
Assert.IsFalse(p.BelongsTo(s));
Assert.IsFalse(p.IsInside(s));
Assert.IsTrue(p.IsOutside(s));
Assert.IsFalse(p.IsOnBoundary(s));
p = new Point3d(1, 2, 0.2); // Point outside
Assert.IsFalse(p.BelongsTo(s));
Assert.IsFalse(p.IsInside(s));
Assert.IsTrue(p.IsOutside(s));
Assert.IsFalse(p.IsOnBoundary(s));
// Resore initial state
GeometRi3D.UseAbsoluteTolerance = mode;
GeometRi3D.Tolerance = tol;
}
public void PointInSegmentRelativeTest()
{
Point3d p = new Point3d(0, 0, 0);
Segment3d s = new Segment3d(p, new Point3d(10, 0, 0));
double tol = GeometRi3D.Tolerance;
bool mode = GeometRi3D.UseAbsoluteTolerance;
GeometRi3D.Tolerance = 0.01;
GeometRi3D.UseAbsoluteTolerance = false;
p = new Point3d(5, 0, 0.05); // Point inside
Assert.IsTrue(p.BelongsTo(s));
Assert.IsTrue(p.IsInside(s));
Assert.IsFalse(p.IsOutside(s));
Assert.IsFalse(p.IsOnBoundary(s));
p = new Point3d(10.05, 0, 0); // Point on boundary
Assert.IsTrue(p.BelongsTo(s));
Assert.IsFalse(p.IsInside(s));
Assert.IsFalse(p.IsOutside(s));
Assert.IsTrue(p.IsOnBoundary(s));
p = new Point3d(1, 0.2, 0); // Point outside
Assert.IsFalse(p.BelongsTo(s));
Assert.IsFalse(p.IsInside(s));
Assert.IsTrue(p.IsOutside(s));
Assert.IsFalse(p.IsOnBoundary(s));
p = new Point3d(10.2, 0, 0); // Point outside
Assert.IsFalse(p.BelongsTo(s));
Assert.IsFalse(p.IsInside(s));
Assert.IsTrue(p.IsOutside(s));
Assert.IsFalse(p.IsOnBoundary(s));
// Resore initial state
GeometRi3D.UseAbsoluteTolerance = mode;
GeometRi3D.Tolerance = tol;
}
public void PointInAlignedBoxRelativeTest()
{
Point3d p = new Point3d(1, 1, 1);
Box3d box = new Box3d(p, 8, 6, 10);
double tol = GeometRi3D.Tolerance;
bool mode = GeometRi3D.UseAbsoluteTolerance;
GeometRi3D.Tolerance = 0.01;
GeometRi3D.UseAbsoluteTolerance = false;
p = new Point3d(2, 2, 2); // Point inside
Assert.IsTrue(p.BelongsTo(box));
Assert.IsTrue(p.IsInside(box));
Assert.IsFalse(p.IsOutside(box));
Assert.IsFalse(p.IsOnBoundary(box));
p = new Point3d(2, 4.1, 2); // Point on side
Assert.IsTrue(p.BelongsTo(box));
Assert.IsFalse(p.IsInside(box));
Assert.IsFalse(p.IsOutside(box));
Assert.IsTrue(p.IsOnBoundary(box));
p = new Point3d(5.1, 4, 6); // Point in corner
Assert.IsTrue(p.BelongsTo(box));
Assert.IsFalse(p.IsInside(box));
Assert.IsFalse(p.IsOutside(box));
Assert.IsTrue(p.IsOnBoundary(box));
p = new Point3d(2, 4.2, 2); // Point outside
Assert.IsFalse(p.BelongsTo(box));
Assert.IsFalse(p.IsInside(box));
Assert.IsTrue(p.IsOutside(box));
Assert.IsFalse(p.IsOnBoundary(box));
// Resore initial state
GeometRi3D.UseAbsoluteTolerance = mode;
GeometRi3D.Tolerance = tol;
}
public void PointInCircleRelativeTest()
{
Point3d p = new Point3d(1, 1, 0);
Circle3d s = new Circle3d(p, 5, new Vector3d(0, 0, 1));
double tol = GeometRi3D.Tolerance;
bool mode = GeometRi3D.UseAbsoluteTolerance;
GeometRi3D.Tolerance = 0.01;
GeometRi3D.UseAbsoluteTolerance = false;
p = new Point3d(2, 2, 0.04); // Point inside
Assert.IsTrue(p.BelongsTo(s));
Assert.IsTrue(p.IsInside(s));
Assert.IsFalse(p.IsOutside(s));
Assert.IsFalse(p.IsOnBoundary(s));
p = new Point3d(1, 6.04, 0); // Point on boundary
Assert.IsTrue(p.BelongsTo(s));
Assert.IsFalse(p.IsInside(s));
Assert.IsFalse(p.IsOutside(s));
Assert.IsTrue(p.IsOnBoundary(s));
p = new Point3d(1, 6.06, 0); // Point outside
Assert.IsFalse(p.BelongsTo(s));
Assert.IsFalse(p.IsInside(s));
Assert.IsTrue(p.IsOutside(s));
Assert.IsFalse(p.IsOnBoundary(s));
p = new Point3d(1, 2, 0.06); // Point outside
Assert.IsFalse(p.BelongsTo(s));
Assert.IsFalse(p.IsInside(s));
Assert.IsTrue(p.IsOutside(s));
Assert.IsFalse(p.IsOnBoundary(s));
// Restore initial state
GeometRi3D.UseAbsoluteTolerance = mode;
GeometRi3D.Tolerance = tol;
}
public void PointInSphereTest()
{
Point3d p = new Point3d(1, 1, 1);
Sphere s = new Sphere(p, 5);
p = new Point3d(2, 2, 2); // Point inside
Assert.IsTrue(p.BelongsTo(s));
Assert.IsTrue(p.IsInside(s));
Assert.IsFalse(p.IsOutside(s));
Assert.IsFalse(p.IsOnBoundary(s));
p = new Point3d(1, 6, 1); // Point on surface
Assert.IsTrue(p.BelongsTo(s));
Assert.IsFalse(p.IsInside(s));
Assert.IsFalse(p.IsOutside(s));
Assert.IsTrue(p.IsOnBoundary(s));
p = new Point3d(1, 6.005, 1); // Point outside
Assert.IsFalse(p.BelongsTo(s));
Assert.IsFalse(p.IsInside(s));
Assert.IsTrue(p.IsOutside(s));
Assert.IsFalse(p.IsOnBoundary(s));
}
public void PointInEllipsoidTest()
{
Point3d p = new Point3d(1, 1, 1);
Ellipsoid s = new Ellipsoid(p, new Vector3d(3, 0, 0), new Vector3d(0, 5, 0), new Vector3d(0, 0, 2));
p = new Point3d(2, 2, 2); // Point inside
Assert.IsTrue(p.BelongsTo(s));
Assert.IsTrue(p.IsInside(s));
Assert.IsFalse(p.IsOutside(s));
Assert.IsFalse(p.IsOnBoundary(s));
p = new Point3d(1, 6, 1); // Point on surface
Assert.IsTrue(p.BelongsTo(s));
Assert.IsFalse(p.IsInside(s));
Assert.IsFalse(p.IsOutside(s));
Assert.IsTrue(p.IsOnBoundary(s));
p = new Point3d(1, 6.005, 1); // Point outside
Assert.IsFalse(p.BelongsTo(s));
Assert.IsFalse(p.IsInside(s));
Assert.IsTrue(p.IsOutside(s));
Assert.IsFalse(p.IsOnBoundary(s));
}