Class Properties

Namespace

MathAssertions.Geometry3D

Assembly

MathAssertions.dll

Geometric-property predicates over MathAssertions.Geometry3D primitives and point sets: triangle degeneracy, point-set collinearity, and point-set coplanarity.

public static class Properties

Inheritance

object

Properties

Inherited Members

object.Equals(object)

object.Equals(object, object)

object.GetHashCode()

object.GetType()

object.MemberwiseClone()

object.ReferenceEquals(object, object)

object.ToString()

Methods

AreCoplanar(ReadOnlySpan<Vector3>, double)

Returns true when every point in points lies on a single plane within tolerance. Sequences with fewer than four points are vacuously coplanar; sequences in which every point is collinear are also coplanar (every line lies on infinitely many planes).

public static bool AreCoplanar(ReadOnlySpan<Vector3> points, double tolerance)

Parameters

points ReadOnlySpan<Vector3>

Points to test.

tolerance double

Maximum allowed perpendicular displacement from the plane. Must be non-negative and not NaN.

Returns

bool

true if all points are coplanar within tolerance.

Remarks

Searches the input for a non-collinear triple and uses it to construct the test plane. If no such triple exists the entire set is collinear, which trivially satisfies coplanarity. The search is at worst quadratic in the number of points when most pairs are collinear with points[0]; for typical test inputs the non-collinear triple is found in the first few iterations.

Exceptions

ArgumentOutOfRangeException

tolerance is NaN or negative.

IsCollinear(ReadOnlySpan<Vector3>, double)

Returns true when every point in points lies on a single line within tolerance. Sequences with fewer than three points are vacuously collinear; sequences in which all points coincide are also collinear.

public static bool IsCollinear(ReadOnlySpan<Vector3> points, double tolerance)

Parameters

points ReadOnlySpan<Vector3>

Points to test.

tolerance double

Maximum allowed perpendicular displacement from the line. Must be non-negative and not NaN.

Returns

bool

true if all points are collinear within tolerance.

Remarks

Picks the first non-trivial direction in the sequence (the first point distinct from points[0] within tolerance) and tests perpendicular distance from that direction for every point. Handling the leading-coincident-points case explicitly avoids the false-true result a naive implementation that locks in points[1] - points[0] would produce when those first two points coincide.

The perpendicular-distance check is computed as |direction × (p - p0)| / |direction|: the cross-product magnitude alone is scaled by |direction|, so comparing it directly to a length-dimensioned tolerance would let a longer baseline silently widen the apparent tolerance. Dividing by the direction magnitude restores the dimensionally correct perpendicular distance from the point to the line through p0.

Exceptions

ArgumentOutOfRangeException

tolerance is NaN or negative.

IsDegenerate(Triangle3D, double)

Returns true when the triangle's area is at most tolerance, indicating collinear or coincident vertices.

public static bool IsDegenerate(this Triangle3D t, double tolerance)

Parameters

t Triangle3D

Triangle to test.

tolerance double

Maximum area considered degenerate. Must be non-negative and not NaN.

Returns

bool

true if t.Area <= tolerance.

Exceptions

ArgumentOutOfRangeException

tolerance is NaN or negative.