Class VectorMath

float2 CapsuleLineIntersectionFactors (

float2	capsuleStart	Center of the capsule's first circle
float2	capsuleDir	Main axis of the capsule. Must be normalized.
float	capsuleLength	Distance betwen the capsule's circle centers.
float2	lineStart	A point on the line
float2	lineDir	The (normalized) direction of the line.
float	radius	The radius of the circle.

)

Calculates the intersection points between a "capsule" (segment expanded by a radius), and a line.

Vector3 ClampMagnitudeXZ (

Vector3	v
float	maxMagnitude

)

Vector3 ClosestPointOnLine (

Vector3	lineStart
Vector3	lineEnd
Vector3	point

)

Returns the closest point on the line.

The line is treated as infinite.

float ClosestPointOnLineFactor (

Vector3	lineStart
Vector3	lineEnd
Vector3	point

)

Factor along the line which is closest to the point.

Returned value is in the range [0,1] if the point lies on the segment otherwise it just lies on the line. The closest point can be calculated using (end-start)*factor + start.

float ClosestPointOnLineFactor (

Int3	lineStart
Int3	lineEnd
Int3	point

)

Factor along the line which is closest to the point.

Returned value is in the range [0,1] if the point lies on the segment otherwise it just lies on the line. The closest point can be calculated using (end-start)*factor + start

float ClosestPointOnLineFactor (

Int2	lineStart
Int2	lineEnd
Int2	point

)

Factor of the nearest point on the segment.

Returned value is in the range [0,1] if the point lies on the segment otherwise it just lies on the line. The closest point can be calculated using (end-start)*factor + start;

Vector3 ClosestPointOnSegment (

Vector3	lineStart
Vector3	lineEnd
Vector3	point

)

Returns the closest point on the segment.

The segment is NOT treated as infinite.

Vector3 ClosestPointOnSegmentXZ (

Vector3	lineStart
Vector3	lineEnd
Vector3	point

)

Returns the closest point on the segment in the XZ plane.

The y coordinate of the result will be the same as the y coordinate of the point parameter.

The segment is NOT treated as infinite.

Vector2 ComplexMultiply (

Vector2	a
Vector2	b

)

Complex number multiplication.

Used to rotate vectors in an efficient way.

Vector2 ComplexMultiplyConjugate (

Vector2	a
Vector2	b

)

Complex number multiplication.

Used to rotate vectors in an efficient way.

float Determinant (

float2	c1
float2	c2

)

Determinant of the 2x2 matrix [c1, c2].

This is useful for many things, like calculating distances between lines and points.

Equivalent to Cross(new float3(c1, 0), new float 3(c2, 0)).z

bool IsClockwiseMarginXZ (

Vector3	a
Vector3	b
Vector3	c

)

Returns if the points a in a clockwise order.

Will return true even if the points are colinear or very slightly counter-clockwise (if the signed area of the triangle formed by the points has an area less than or equals to float.Epsilon)

bool IsClockwiseOrColinear (

Int2	a
Int2	b
Int2	c

)

Returns true if the points a in a clockwise order or if they are colinear.

bool IsClockwiseOrColinearXZ (

Int3	a
Int3	b
Int3	c

)

Returns true if the points a in a clockwise order or if they are colinear.

bool IsClockwiseXZ (

Vector3	a
Vector3	b
Vector3	c

)

Returns if the points a in a clockwise order.

bool IsClockwiseXZ (

Int3	a
Int3	b
Int3	c

)

Returns if the points a in a clockwise order.

bool IsColinear (

Vector3	a
Vector3	b
Vector3	c

)

Returns if the points are colinear (lie on a straight line)

bool IsColinear (

Vector2	a
Vector2	b
Vector2	c

)

Returns if the points are colinear (lie on a straight line)

bool IsColinearAlmostXZ (

Int3	a
Int3	b
Int3	c

)

Returns if the points are colinear (lie on a straight line)

bool IsColinearXZ (

Int3	a
Int3	b
Int3	c

)

Returns if the points are colinear (lie on a straight line)

bool IsColinearXZ (

Vector3	a
Vector3	b
Vector3	c

)

Returns if the points are colinear (lie on a straight line)

float LineCircleIntersectionFactor (

Vector3	circleCenter
Vector3	linePoint1
Vector3	linePoint2
float	radius

)

Intersection of a line and a circle.

Returns the greatest t such that segmentStart+t*(segmentEnd-segmentStart) lies on the circle.

In case the line does not intersect with the circle, the closest point on the line to the circle will be returned.

bool LineCircleIntersectionFactors (

float2	point	A point on the line
float2	direction	The normalized direction of the line
float	radius	The radius of the circle at the origin.
out float	t1	The first intersection (if any).
out float	t2	The second intersection (if any).

)

Calculates the two intersection points (point + direction*t) on the line where it intersects with a circle at the origin.

t1 will always be less than or equal to t2 if there are intersections.

Returns false if there are no intersections.

Vector3 LineDirIntersectionPointXZ (

Vector3	start1
Vector3	dir1
Vector3	start2
Vector3	dir2

)

Intersection point between two infinite lines.

Note that start points and directions are taken as parameters instead of start and end points. Lines are treated as infinite. If the lines are parallel 'start1' will be returned. Intersections are calculated on the XZ plane.

Vector3 LineDirIntersectionPointXZ (

Vector3	start1
Vector3	dir1
Vector3	start2
Vector3	dir2
out bool	intersects

)

Intersection point between two infinite lines.

Note that start points and directions are taken as parameters instead of start and end points. Lines are treated as infinite. If the lines are parallel 'start1' will be returned. Intersections are calculated on the XZ plane.

bool LineIntersectionFactorXZ (

Int3	start1
Int3	end1
Int3	start2
Int3	end2
out float	factor1
out float	factor2

)

Returns the intersection factors for line 1 and line 2.

The intersection factors is a distance along the line start - end where the other line intersects it.
intersectionPoint = start1 + factor1 * (end1-start1)
intersectionPoint2 = start2 + factor2 * (end2-start2)
Lines are treated as infinite.
false is returned if the lines are parallel and true if they are not. Only the XZ coordinates are used.

bool LineIntersectionFactorXZ (

Vector3	start1
Vector3	end1
Vector3	start2
Vector3	end2
out float	factor1
out float	factor2

)

Returns the intersection factors for line 1 and line 2.

The intersection factors is a distance along the line start - end where the other line intersects it.
intersectionPoint = start1 + factor1 * (end1-start1)
intersectionPoint2 = start2 + factor2 * (end2-start2)
Lines are treated as infinite.
false is returned if the lines are parallel and true if they are not. Only the XZ coordinates are used.

float LineIntersectionFactorXZ (

Vector3	start1
Vector3	end1
Vector3	start2
Vector3	end2

)

Returns the intersection factor for line 1 with line 2.

The intersection factor is a distance along the line start1 - end1 where the line start2 - end2 intersects it.
intersectionPoint = start1 + intersectionFactor * (end1-start1)
. Lines are treated as infinite.
-1 is returned if the lines are parallel (note that this is a valid return value if they are not parallel too)

Vector2 LineIntersectionPoint (

Vector2	start1
Vector2	end1
Vector2	start2
Vector2	end2

)

Returns the intersection point between the two lines.

Lines are treated as infinite. start1 is returned if the lines are parallel

Vector2 LineIntersectionPoint (

Vector2	start1
Vector2	end1
Vector2	start2
Vector2	end2
out bool	intersects

)

Returns the intersection point between the two lines.

Lines are treated as infinite. start1 is returned if the lines are parallel

Vector3 LineIntersectionPointXZ (

Vector3	start1
Vector3	end1
Vector3	start2
Vector3	end2

)

Returns the intersection point between the two lines.

Lines are treated as infinite. start1 is returned if the lines are parallel

Vector3 LineIntersectionPointXZ (

Vector3	start1
Vector3	end1
Vector3	start2
Vector3	end2
out bool	intersects

)

Returns the intersection point between the two lines.

Lines are treated as infinite. start1 is returned if the lines are parallel

bool LineLineIntersectionFactor (

float2	start1
float2	dir1
float2	start2
float2	dir2
out float	t

)

Calculates the point start1 + dir1*t where the two infinite lines intersect.

Returns false if the lines are close to parallel.

bool LineLineIntersectionFactors (

float2	start1
float2	dir1
float2	start2
float2	dir2
out float	factor1
out float	factor2

)

Calculates the point start1 + dir1*factor1 == start2 + dir2*factor2 where the two infinite lines intersect.

Returns false if the lines are close to parallel.

float LineRayIntersectionFactorXZ (

Int3	start1
Int3	end1
Int3	start2
Int3	end2

)

Returns the intersection factor for line 1 with ray 2.

The intersection factors is a factor distance along the line start - end where the other line intersects it.
intersectionPoint = start1 + factor * (end1-start1)
Lines are treated as infinite.
The second "line" is treated as a ray, meaning only matches on start2 or forwards towards end2 (and beyond) will be returned If the point lies on the wrong side of the ray start, Nan will be returned.

NaN is returned if the lines are parallel.

float MagnitudeXZ (

Vector3

v

)

Vector3 Normalize (

Vector3	v
out float	magnitude

)

Normalize vector and also return the magnitude.

This is more efficient than calculating the magnitude and normalizing separately

Vector2 Normalize (

Vector2	v
out float	magnitude

)

Normalize vector and also return the magnitude.

This is more efficient than calculating the magnitude and normalizing separately

bool RaySegmentIntersectXZ (

Int3	start1
Int3	end1
Int3	start2
Int3	end2

)

Returns if the ray (start1, end1) intersects the segment (start2, end2).

false is returned if the lines are parallel. Only the XZ coordinates are used.

bool ReversesFaceOrientations (

Matrix4x4

matrix

)

True if the matrix will reverse orientations of faces.

Scaling by a negative value along an odd number of axes will reverse the orientation of e.g faces on a mesh. This must be counter adjusted by for example the recast rasterization system to be able to handle meshes with negative scales properly.

We can find out if they are flipped by finding out how the signed volume of a unit cube is transformed when applying the matrix

If the (signed) volume turns out to be negative that also means that the orientation of it has been reversed.

bool ReversesFaceOrientationsXZ (

Matrix4x4

matrix

)

True if the matrix will reverse orientations of faces in the XZ plane.

Almost the same as ReversesFaceOrientations, but this method assumes that scaling a face with a negative scale along the Y axis does not reverse the orientation of the face.

This is used for navmesh cuts.

Scaling by a negative value along one axis or rotating it so that it is upside down will reverse the orientation of the cut, so we need to be reverse it again as a countermeasure. However if it is flipped along two axes it does not need to be reversed. We can handle all these cases by finding out how a unit square formed by our forward axis and our rightward axis is transformed in XZ space when applying the local to world matrix. If the (signed) area of the unit square turns out to be negative that also means that the orientation of it has been reversed. The signed area is calculated using a cross product of the vectors.

bool RightOrColinear (

Vector2	a
Vector2	b
Vector2	p

)

Returns if p lies on the right side of the line a - b.

Also returns true if the points are colinear.

bool RightOrColinear (

Int2	a
Int2	b
Int2	p

)

Returns if p lies on the right side of the line a - b.

Also returns true if the points are colinear.

bool RightOrColinearXZ (

Vector3	a
Vector3	b
Vector3	p

)

Returns if p lies on the left side of the line a - b.

Uses XZ space. Also returns true if the points are colinear.

bool RightOrColinearXZ (

Int3	a
Int3	b
Int3	p

)

Returns if p lies on the left side of the line a - b.

Uses XZ space. Also returns true if the points are colinear.

bool RightXZ (

Vector3	a
Vector3	b
Vector3	p

)

Returns if p lies on the right side of the line a - b.

Uses XZ space. Does not return true if the points are colinear.

bool RightXZ (

Int3	a
Int3	b
Int3	p

)

Returns if p lies on the right side of the line a - b.

Uses XZ space. Does not return true if the points are colinear.

Vector3 SegmentIntersectionPointXZ (

Vector3	start1
Vector3	end1
Vector3	start2
Vector3	end2
out bool	intersects

)

Returns the intersection point between the two line segments in XZ space.

Lines are NOT treated as infinite. start1 is returned if the line segments do not intersect The point will be returned along the line [start1, end1] (this matters only for the y coordinate).

bool SegmentIntersectsBounds (

Bounds	bounds
Vector3	a
Vector3	b

)

Does the line segment intersect the bounding box.

The line is NOT treated as infinite.

bool SegmentsIntersect (

Int2	start1
Int2	end1
Int2	start2
Int2	end2

)

Returns if the line segment start2 - end2 intersects the line segment start1 - end1.

If only the endpoints coincide, the result is undefined (may be true or false).

bool SegmentsIntersectXZ (

Int3	start1
Int3	end1
Int3	start2
Int3	end2

)

Returns if the line segment start2 - end2 intersects the line segment start1 - end1.

If only the endpoints coincide, the result is undefined (may be true or false).

bool SegmentsIntersectXZ (

Vector3	start1
Vector3	end1
Vector3	start2
Vector3	end2

)

Returns if the two line segments intersects.

The lines are NOT treated as infinite (just for clarification)

Side SideXZ (

Int3	a
Int3	b
Int3	p

)

Returns which side of the line a - b that p lies on.

Uses XZ space.

long SignedTriangleAreaTimes2XZ (

Int3	a
Int3	b
Int3	c

)

Signed area of a triangle in the XZ plane multiplied by 2.

This will be negative for clockwise triangles and positive for counter-clockwise ones

float SignedTriangleAreaTimes2XZ (

Vector3	a
Vector3	b
Vector3	c

)

Signed area of a triangle in the XZ plane multiplied by 2.

This will be negative for clockwise triangles and positive for counter-clockwise ones.

float SqrDistancePointSegment (

Vector3	a
Vector3	b
Vector3	p

)

Returns the squared distance between p and the segment a-b.

The line is not considered infinite.

float SqrDistancePointSegmentApproximate (

int	x
int	z
int	px
int	pz
int	qx
int	qz

)

Returns the approximate shortest squared distance between x,z and the segment p-q.

The segment is not considered infinite. This function is not entirely exact, but it is about twice as fast as DistancePointSegment2.

float SqrDistancePointSegmentApproximate (

Int3	a
Int3	b
Int3	p

)

Returns the approximate shortest squared distance between x,z and the segment p-q.

The segment is not considered infinite. This function is not entirely exact, but it is about twice as fast as DistancePointSegment2.

float SqrDistanceSegmentSegment (

Vector3	s1
Vector3	e1
Vector3	s2
Vector3	e2

)

3D minimum distance between 2 segments.

Input: two 3D line segments S1 and S2

float SqrDistanceXZ (

Vector3	a
Vector3	b

)

Squared distance between two points in the XZ plane.