Geometric

Description

static class Tinman.Core.Math.Geometric

Helper class for computing geometric intersections.

Public / Methods

AreaPolygon

_2 overloads

public static method AreaPolygon¹ → (3)

v ⁱⁿ : Vec2D [ ]: [not-null]
The polygon vertices.
a ⁱⁿ : int32: [0..v.Length-1]
Index of first polygon vertex.
b ⁱⁿ : int32: [0..v.Length-1]
Index of last polygon vertex.
returns → float64: The signed area of the simple polygon.

Computes the signed area of the given simple polygon.

The polygon is defined as follows:

v[a    ] := first polygon vertex
v[a + n] := n-th polygon vertex
v[b    ] := last polygon vertex (not equal to first)

where b - a >= 2
      b - a >= n >= 0

Inverting the order of the polygon vertices will flip the sign of the area value. For a standard Cartesian coordinate system (X-axis points to the right, Y-axis points upwards), clockwise polygons have negative area values and counter-clockwise polygons have positive area values.

public static method AreaPolygon² → (4)

v ⁱⁿ : Vec2D [ ]: [not-null]
The polygon vertices.
i ⁱⁿ : int32 [ ]: [not-null]
The polygon vertex indices.
a ⁱⁿ : int32: [0..i.Length-1]
Index of first polygon vertex index.
b ⁱⁿ : int32: [0..i.Length-1]
Index of last polygon vertex index.
returns → float64: The signed area of the simple polygon.

Computes the signed area of the given simple polygon.

The polygon is defined as follows:

v[i[a    ]] := first polygon vertex
v[i[a + n]] := n-th polygon vertex
v[i[b    ]] := last polygon vertex (not equal to first)

where b - a >= 2
      b - a >= n >= 0

AreaTriangle

_4 overloads

[Pure]
public static method AreaTriangle¹ → (3)

v1 ⁱⁿ : Vec2D: First vertex of triangle.
v2 ⁱⁿ : Vec2D: Second vertex of triangle.
v3 ⁱⁿ : Vec2D: Third vertex of triangle.
returns → float64: The signed area of the triangle.

Computes the area of the given triangle.

[Pure]
public static method AreaTriangle² → (6)

x1 ⁱⁿ : float64: X-coordinate of first vertex of triangle.
y1 ⁱⁿ : float64: Y-coordinate of first vertex of triangle.
x2 ⁱⁿ : float64: X-coordinate of second vertex of triangle.
y2 ⁱⁿ : float64: Y-coordinate of second vertex of triangle.
x3 ⁱⁿ : float64: X-coordinate of third vertex of triangle.
y3 ⁱⁿ : float64: Y-coordinate of third vertex of triangle.
returns → float64: The signed area of the triangle.

Computes the area of the given triangle.

[Pure]
public static method AreaTriangle³ → (3)

v1 ⁱⁿ : Vec3D: First vertex of triangle.
v2 ⁱⁿ : Vec3D: Second vertex of triangle.
v3 ⁱⁿ : Vec3D: Third vertex of triangle.
returns → float64: The area of the triangle.

Computes the area of the given triangle.

[Pure]
public static method AreaTriangle⁴ → (9)

x1 ⁱⁿ : float64: X-coordinate of first vertex of triangle.
y1 ⁱⁿ : float64: Y-coordinate of first vertex of triangle.
z1 ⁱⁿ : float64: Z-coordinate of first vertex of triangle.
x2 ⁱⁿ : float64: X-coordinate of second vertex of triangle.
y2 ⁱⁿ : float64: Y-coordinate of second vertex of triangle.
z2 ⁱⁿ : float64: Z-coordinate of second vertex of triangle.
x3 ⁱⁿ : float64: X-coordinate of third vertex of triangle.
y3 ⁱⁿ : float64: Y-coordinate of third vertex of triangle.
z3 ⁱⁿ : float64: Z-coordinate of third vertex of triangle.
returns → float64: The area of the triangle.

Computes the area of the given triangle.

BestBasisVector

[Pure]
public static method BestBasisVector → (1)

v ⁱⁿ : Vec3D: The vector.
returns → Vec3D: The basis vector with the smallest absolute dot product with v ⁱⁿ.

Returns the basis vector (X, Y or Z) that has the highest amount of perpendicularity to the given vector.

CartesianToSpherical

_2 overloads

[Pure]
public static method CartesianToSpherical¹ → (1)

cartesian ⁱⁿ : Vec3D: The cartesian coordinates.
returns → Vec3D: The spherical coordinates.

Converts the given cartesian coordinates into spherical coordinates.

The components of the returned vector have the following semantic:

spherical.X := radius (distance to origin).
spherical.Y := azimuthal angle (angle from positive X-axis in radians) in the range [-PI..PI].
spherical.Z := polar angle (angle from positive Z-axis in radians) in the range [0..PI].

[Pure]
public static method CartesianToSpherical² → (3)

x ⁱⁿ : float64: The cartesian X-coordinate.
y ⁱⁿ : float64: The cartesian Y-coordinate.
z ⁱⁿ : float64: The cartesian Z-coordinate.
returns → Vec3D: The spherical coordinates.

Converts the given cartesian coordinates into spherical coordinates.

The components of the returned vector have the following semantic:

spherical.X := radius (distance to origin).
spherical.Y := azimuthal angle (angle from positive X-axis in radians) in the range [-PI..PI].
spherical.Z := polar angle (angle from positive Z-axis in radians) in the range [0..PI].

CheckIntersectionOfLineSegments

_2 overloads

[Pure]
public static method CheckIntersectionOfLineSegments¹ → (4)

v1 ⁱⁿ : Vec2D: Start of first line segment.
v2 ⁱⁿ : Vec2D: End of first line segment.
v3 ⁱⁿ : Vec2D: Start of second line segment.
v4 ⁱⁿ : Vec2D: End of second line segment.
returns → bool: true if the line segments intersect, false if not.

Checks if the given line segments intersect.

[Pure]
public static method CheckIntersectionOfLineSegments² → (8)

x1 ⁱⁿ : float64: X-coordinate of start of first line segment.
y1 ⁱⁿ : float64: Y-coordinate of start of first line segment.
x2 ⁱⁿ : float64: X-coordinate of end of first line segment.
y2 ⁱⁿ : float64: Y-coordinate of end of first line segment.
x3 ⁱⁿ : float64: X-coordinate of start of second line segment.
y3 ⁱⁿ : float64: X-coordinate of start of second line segment.
x4 ⁱⁿ : float64: X-coordinate of end of second line segment.
y4 ⁱⁿ : float64: X-coordinate of end of second line segment.
returns → bool: true if the line segments intersect, false if not.

Checks if the given line segments intersect.

ConeFitAngle

[Pure]
public static method ConeFitAngle → (3)

x ⁱⁿ : float64: X-coordinate of sphere center.
y ⁱⁿ : float64: Y-coordinate of sphere center.
r ⁱⁿ : float64: Radius of sphere.
returns → float64: The opening angle of the cone, in radians. Will be Maths.NanD if x ⁱⁿ, y ⁱⁿ or r ⁱⁿ is negative or if the cone apex is inside of the sphere.

Computes the opening angle of the right circular cone having the smallest volume that contains the given sphere.

The cone apex is at (0,0,0). The cone axis is collinear to (1,0,0). The sphere center is at (x ⁱⁿ, y ⁱⁿ, 0).

ConeFitDistance

[Pure]
public static method ConeFitDistance → (4)

a ⁱⁿ : float64: The cone opening angle, in radians.
x ⁱⁿ : float64: X-coordinate of sphere center.
y ⁱⁿ : float64: Y-coordinate of sphere center.
r ⁱⁿ : float64: Radius of sphere.
returns → float64: The translation along the X-axis that must be applied to the cone apex in order to make the cone touch the sphere, while containing it. Will be Maths.NanD if y ⁱⁿ or r ⁱⁿ is negative or if a ⁱⁿ is outside of the range ]0..pi[.

Computes the translation that must be applied to the given right circular to make it contain the given sphere, while only touching it in a single point.

The cone apex is at (0,0,0). The cone axis is collinear to (1,0,0). The sphere center is at (x ⁱⁿ, y ⁱⁿ, 0).

DistanceLineToLine

[Pure]
public static method DistanceLineToLine → (4)

s1 ⁱⁿ : Vec3D: Point on first line.
v1 ⁱⁿ : Vec3D: Direction vector of first line.
s2 ⁱⁿ : Vec3D: Point on second line.
v2 ⁱⁿ : Vec3D: Direction vector of second line.
returns → Vec2D: The coefficient vector for computing the two nearest points on both lines:

p1 = s1 + v1 * X
p2 = s2 + v2 * Y

Computes the pair of nearest points on two lines.

DistancePointToHorizon

[Pure]
public static method DistancePointToHorizon → (2)

point ⁱⁿ : Vec3D: The point coordinates.
radius ⁱⁿ : float64: [>0]
The sphere radius.
returns → float64: The distance to the horizon, in terrain-space.

Computes the distance from the given point to the horizon circle on a sphere centered at the coordinate origin and having the given radius.

DistancePointToLine

public static method DistancePointToLine → (3)

p ⁱⁿ : Vec3D: The point.
s ⁱⁿ : Vec3D: A point on the line.
v ⁱⁿ : Vec3D: Unit-length direction vector of the line.
returns → Vec3D: The point on the line that is nearest to p ⁱⁿ.

Returns the distance of the given point to the specified line.