struct Cuboid in Tinman.Core.Math

A cuboid.

struct

Cuboid

Remarks

The vertices of the cuboid are defined as follows, based on the unit cube:

   2-------6                c0 := (0, 0, 0)
  /.      /|      Y+        c1 := (0, 0, 1)
 / .     / |      |         c2 := (0, 1, 0)
3-------7  |      +-- X+    c3 := (0, 1, 1)
|  0....|..4     /          c4 := (1, 0, 0)
| .     | /     Z+          c5 := (1, 0, 1)
|.      |/                  c6 := (1, 1, 0)
1-------5                   c7 := (1, 1, 1)

where the transformation of a point A in unit cube space and a point B in world-space is defined as this:

A' = Orientation * A + Origin
B' = Orientation' * (B - Origin)

where A' and B' are the transformed points in world-space resp. unit cube space, and Orientation' is the transpose of Orientation.

Serialization

Serializer

The serialization helper object for values of Cuboid.

public static readonly field	Serializer
type	ITypeSerializer<Cuboid>

Public / Constants

Unit

The unit cube.

public static readonly field	Unit
type	Cuboid

Public / Attributes

Orientation

The matrix that transforms from the unit cube to world-space.

public readonly field	Orientation
type	Mat3D

Origin

Origin of the unit cube, in world-space.

public readonly field	Origin
type	Vec3D

Public / Constructors

Cuboid

Creates a new instance of Cuboid.

public constructor	Cuboid (Vec3D origin, Mat3D orientation)
params	origin		Origin of the unit cube, in world-space.
	orientation		Affine matrix that transforms from the unit cube to world-space.

FromMatrix

Creates a new instance of Cuboid.

[Pure]
public static method	FromMatrix (Mat4D matrix)
type	Cuboid
params	matrix		A matrix that transforms from the unit cube to world-space.

See also:

ToMatrix

FromPoints

Creates a new instance of Cuboid.

[Pure]
public static method	FromPoints (Vec3D v0, Vec3D v4, Vec3D v2, Vec3D v1)
type	Cuboid
params	v0		Coordinates of corner vertex c0 (origin, see remarks).
	v4		Coordinates of corner vertex c4 (X-axis, see remarks).
	v2		Coordinates of corner vertex c2 (Y-axis, see remarks).
	v1		Coordinates of corner vertex c1 (Z-axis, see remarks).

See also:

ToPoint

Public / Methods

RangeZ

Returns the Z-range of this cuboid along the given ray.

[Pure]
public method	RangeZ (Vec3D p, Vec3D v)
type	RangeD
params	p		The ray origin.
	v		The unit-length ray direction vector.
returns			The Z-range.

ToMatrix

Returns a matrix that transforms from the unit cube to world-space.

[Pure]
public method	ToMatrix ()
type	Mat4D
returns			The transformation matrix.

See also:

FromMatrix

ToPoint

Returns the world-space coordinates of the given cuboid corner vertex.

[Pure]
public method	ToPoint (int32 n)
type	Vec3D
params	n		The corner vertex (see remarks).
returns			The world-space coordinates of the corner vertex.

See also:

FromPoints

Transform

Transforms this cuboid.

[Pure]
public method	Transform (Mat4D matrix)
type	Cuboid
params	matrix		The transformation matrix.
returns			The transformed cuboid.