AffineTransform

Description

struct Tinman.Terrain.Util.AffineTransform

Represents an affine transformation matrix that is decomposable into translation, rotation / reflection, and uniform scaling.

Public / Constants

Identity

public static readonly attribute Identity → (AffineTransform)

The identity transform.

Public / Constructors

Affine​Transform

7 overloads

public constructor AffineTransform1 → (1)

translation in : Vec3D

The translation component of the affine transform.

Creates a new instance of AffineTransform.

public constructor AffineTransform2 → (1)

rotation in : Mat3D

The affine matrix that represents the rotation component of the affine transform.

Creates a new instance of AffineTransform.

public constructor AffineTransform3 → (1)

scaling in : float64

The uniform scale factor of the affine transform.

Creates a new instance of AffineTransform.

public constructor AffineTransform4 → (2)

translation in : Vec3D

The translation component of the affine transform.

rotation in : Mat3D

The matrix that represents the rotation / reflection component of the affine transform.

Creates a new instance of AffineTransform.

public constructor AffineTransform5 → (2)

translation in : Vec3D

The translation component of the affine transform.

scaling in : float64

The uniform scale factor of the affine transform.

Creates a new instance of AffineTransform.

public constructor AffineTransform6 → (2)

rotation in : Mat3D

The matrix that represents the rotation / reflection component of the affine transform.

scaling in : float64

The uniform scale factor of the affine transform.

Creates a new instance of AffineTransform.

public constructor AffineTransform7 → (3)

translation in : Vec3D

The translation component of the affine transform.

rotation in : Mat3D

The matrix that represents the rotation / reflection component of the affine transform.

scaling in : float64

The uniform scale factor of the affine transform.

Creates a new instance of AffineTransform.

From​Matrix

3 overloads

[Pure]
public static method FromMatrix1 → (2)

matrix in : Mat3D

The matrix for which to create an affine transform.

translation opt : Vec3D = default(Vec3D)

The translation component of the affine transform.

returns → AffineTransform

The affine transform.

Creates a new instance of AffineTransform.

The non-uniform scaling part of matrix in will be dropped.

[Pure]
public static method FromMatrix2 → (1)

matrix in : Mat4D

The matrix for which to create an affine transform.

returns → AffineTransform

The affine transform.

Creates a new instance of AffineTransform.

The non-uniform scaling and homogeneous parts of matrix in will be dropped.

[Pure]
public static method FromMatrix3 → (2)

matrix in : Mat4D

The matrix for which to create an affine transform.

remainder out : Mat4D

The non-affine transformation part that remains (will be written to after reading from matrix in):

M = A x R

where M is matrix in, A is the returned affine transformation and R is remainder out.

returns → AffineTransform

The affine transform.

Creates a new instance of AffineTransform.

The non-uniform scaling and homogeneous parts of matrix in will be stored into remainder out.

Public / Methods

Append

[Pure]
public method Append → (1)

transform in : AffineTransform

The affine transform to append.

returns → AffineTransform

The resulting affine transform, which applies this affine transform first and the given transform in afterwards. This is opposite to matrix multiplication:

FromMatrix(transform.ToMatrix().Mul(this.ToMatrix()))

Appends the given affine transform to this one.

Append​Inv

[Pure]
public method AppendInv → (1)

transform in : AffineTransform

The affine transform which inverse to append.

returns → AffineTransform

The resulting affine transform, which applies this affine transform first and the inverse of the given transform in afterwards. This is opposite to matrix multiplication:

FromMatrix(transform.ToMatrixInv().Mul(this.ToMatrix()))

Appends the inverse of the given affine transform to this one.

Equals​Almost

[Pure]
public method EqualsAlmost → (1)

other in : AffineTransform

The other transform.

returns → bool

true if both transforms are similar, false if they are not.

Checks if this transform and the given one are similar but necessarily equal.

See also

Maths.Similar2

Rotate

[Pure]
public method Rotate → (1)

matrix in : Mat3D

The rotation matrix to apply.

returns → AffineTransform

The resulting affine transform.

Applies the given rotation matrix in to this affine transform.

Using this method is equivalent to calling Append on this affine transform, passing a rotation-only transform created from matrix in.

See also

AffineTransform.Scale
AffineTransform.Translate

Rotate​Keep​Translation

[Pure]
public method RotateKeepTranslation → (1)

matrix in : Mat3D

The rotation matrix to apply.

returns → AffineTransform

The resulting affine transform.

Applies the given rotation matrix in to this affine transform.

Using this method is not (!) equivalent to calling Append on this affine transform, passing a rotation-only transform created from matrix in, because Translation is not modified.

See also

AffineTransform.ScaleKeepTranslation

Scale

[Pure]
public method Scale → (1)

factor in : float64

The scale factor to apply.

returns → AffineTransform

The resulting affine transform.

Applies the given scale factor in to this affine transform.

Using this method is equivalent to calling Append on this affine transform, passing a scaling-only transform created from factor in.

See also

AffineTransform.Rotate
AffineTransform.Translate

Scale​Keep​Translation

[Pure]
public method ScaleKeepTranslation → (1)

factor in : float64

The scale factor to apply.

returns → AffineTransform

The resulting affine transform.

Applies the given scale factor in to this affine transform.

Using this method is not (!) equivalent to calling Append on this affine transform, passing a scaling-only transform created from factor in, because Translation is not modified.

To​Matrix

[Pure]
public method ToMatrix → ()

returns → Mat4D

The matrix.

Converts this affine transform into a matrix.

To​Matrix​Inv

[Pure]
public method ToMatrixInv → ()

returns → Mat4D

The matrix.

Converts the inverse of this affine transform into a matrix.

Transform​Box

[Pure]
public method TransformBox → (1)

box in : Box3D

The axis-aligned bounding box.

returns → Box3D

The transformed axis-aligned bounding box.

Transforms the given axis-aligned bounding box with this affine transformation.

Transform​Box​Inv

[Pure]
public method TransformBoxInv → (1)

box in : Box3D

The axis-aligned bounding box.

returns → Box3D

The transformed axis-aligned bounding box.

Transforms the given axis-aligned bounding box with the inverse of this affine transformation.

Transform​Point

2 overloads

[Pure]
public method TransformPoint1 → (1)

point in : Vec3D

The point.

returns → Vec3D

The transformed point.

Transforms the given point with this affine transformation.

[Pure]
public method TransformPoint2 → (3)

x in : float64

X-coordinate of the point.

y in : float64

Y-coordinate of the point.

z in : float64

Z-coordinate of the point.

returns → Vec3D

The transformed point.

Transforms the given point with this affine transformation.

Transform​Point​Inv

2 overloads

[Pure]
public method TransformPointInv1 → (3)

x in : float64

X-coordinate of the point.

y in : float64

Y-coordinate of the point.

z in : float64

Z-coordinate of the point.

returns → Vec3D

The transformed point.

Transforms the given point with the inverse of this affine transformation.

[Pure]
public method TransformPointInv2 → (1)

point in : Vec3D

The point.

returns → Vec3D

The transformed point.

Transforms the given point with the inverse of this affine transformation.

Transform​Range

[Pure]
public method TransformRange → (1)

range in : RangeD

The range.

returns → RangeD

The transformed range.

Transforms the given range with this affine transformation.

Transform​Range​Inv

[Pure]
public method TransformRangeInv → (1)

range in : RangeD

The range.

returns → RangeD

The transformed range.

Transforms the given range with the inverse of this affine transformation.

Transform​Ray

[Pure]
public method TransformRay → (1)

ray in : Ray

The ray.

returns → Ray

The transformed ray.

Transforms the given ray.

Transform​Ray​Inv

[Pure]
public method TransformRayInv → (1)

ray in : Ray

The ray.

returns → Ray

The transformed ray.

Transforms the given ray with the inverse of this affine transformation.

Transform​Scalar

[Pure]
public method TransformScalar → (1)

v in : float64

The scalar value.

returns → float64

The transformed scalar.

Transforms the given scalar with this affine transformation.

Transform​Scalar​Inv

[Pure]
public method TransformScalarInv → (1)

v in : float64

The scalar value.

returns → float64

The transformed scalar.

Transforms the given scalar with the inverse of this affine transformation.

Transform​Sphere

[Pure]
public method TransformSphere → (1)

sphere in : Sphere

The bounding sphere.

returns → Sphere

The transformed bounding sphere box.

Transforms the given bounding sphere with this affine transformation.

Transform​Sphere​Inv

[Pure]
public method TransformSphereInv → (1)

sphere in : Sphere

The bounding sphere.

returns → Sphere

The transformed bounding sphere box.

Transforms the given bounding sphere with the inverse of this affine transformation.

Transform​Vector

2 overloads

[Pure]
public method TransformVector1 → (1)

vector in : Vec3D

The vector.

returns → Vec3D

The transformed vector.

Transforms the given vector with this affine transformation.

[Pure]
public method TransformVector2 → (3)

x in : float64

X-component of the vector.

y in : float64

Y-component of the vector.

z in : float64

Z-component of the vector.

returns → Vec3D

The transformed vector.

Transforms the given vector with this affine transformation.

Transform​Vector​Inv

2 overloads

[Pure]
public method TransformVectorInv1 → (1)

vector in : Vec3D

The vector.

returns → Vec3D

The transformed vector.

Transforms the given vector with the inverse of this affine transformation.

[Pure]
public method TransformVectorInv2 → (3)

x in : float64

X-component of the vector.

y in : float64

Y-component of the vector.

z in : float64

Z-component of the vector.

returns → Vec3D

The transformed vector.

Transforms the given vector with the inverse of this affine transformation.

Translate

[Pure]
public method Translate → (1)

amount in : Vec3D

The translation amount to apply

returns → AffineTransform

The resulting affine transform.

Add the given translation amount in to Translation

Using this method is equivalent to calling Append on this affine transform, passing a translation-only transform created from amount in.

See also

AffineTransform.Rotate
AffineTransform.Scale

Public / Attributes

Determinant

public attribute Determinant → (get)

value : float64

The sign of the value of Mat4D.Determinant of ToMatrix.

Returns the sign of the determinant of the matrix that corresponds to this affine transformation.

Inverse

public attribute Inverse → (get)

value : AffineTransform

The inverse transformation.

Returns the inverse of this transformation.

See also

AffineTransform.AppendInv
AffineTransform.ToMatrixInv
AffineTransform.TransformBoxInv
AffineTransform.TransformPointInv2
AffineTransform.TransformRangeInv
AffineTransform.TransformRayInv
AffineTransform.TransformScalarInv
AffineTransform.TransformSphereInv
AffineTransform.TransformVectorInv1

Rotation

public readonly attribute Rotation → (Mat3D)

The orthonormal matrix that represents the rotation / reflection component of the transform.

Scaling

public readonly attribute Scaling → (float64)

The uniform scale factor of the transform.

Translation

public readonly attribute Translation → (Vec3D)

The translation component of the transform.