Euclidean2d
Represents a Rigid Transformation (or Rigid Body Transformation) in 2D that is composed of a 2D rotation Rot and a subsequent translation by a 2D vector Trans. This is also called an Euclidean Transformation and is a length preserving Transformation.
Constructors
| Constructor | Description |
new(rot, trans)
Signature: (rot:Rot2d * trans:V2d) -> unit
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Creates a rigid transformation from a rotation and a (subsequent) translation . |
new(rot, trans)
Signature: (rot:M22d * trans:V2d) -> unit
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Creates a rigid transformation from a rotation matrix and a (subsequent) translation . |
new(trafo)
Signature: trafo:Trafo2d -> unit
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Creates a rigid transformation from a trafo . |
Instance members
| Instance member | Description |
Equals(other)
Signature: other:obj -> bool
Modifiers: abstract |
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GetHashCode()
Signature: unit -> int
Modifiers: abstract |
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Inverse
Signature: Euclidean2d
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Gets the (multiplicative) inverse of this Euclidean transformation. [Rot^T,-Rot^T Trans] |
Invert()
Signature: unit -> unit
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Inverts this rigid transformation (multiplicative inverse). this = [Rot^T,-Rot^T Trans] |
InvTransformDir(v)
Signature: v:V2d -> V2d
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Transforms direction vector v (v.w is presumed 0.0) by the inverse of this rigid transformation. Actually, only the rotation is used. |
InvTransformPos(p)
Signature: p:V2d -> V2d
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Transforms point p (p.w is presumed 1.0) by the inverse of this rigid transformation. |
IsInvalid
Signature: bool
Modifiers: abstract |
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IsValid
Signature: bool
Modifiers: abstract |
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ToString()
Signature: unit -> string
Modifiers: abstract |
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TransformDir(v)
Signature: v:V2d -> V2d
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Transforms direction vector v (v.w is presumed 0.0) by this rigid transformation. Actually, only the rotation is used. |
TransformPos(p)
Signature: p:V2d -> V2d
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Transforms point p (p.w is presumed 1.0) by this rigid transformation. |
Static members
| Static member | Description |
ApproxEqual(r0, r1)
Signature: (r0:Euclidean2d * r1:Euclidean2d) -> bool
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ApproxEqual(r0, r1, angleTol, posTol)
Signature: (r0:Euclidean2d * r1:Euclidean2d * angleTol:float * posTol:float) -> bool
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InvTransformDir(r, v)
Signature: (r:Euclidean2d * v:V2d) -> V2d
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Transforms direction vector v (v.w is presumed 0.0) by the inverse of the rigid transformation r. Actually, only the rotation is used. |
InvTransformPos(r, p)
Signature: (r:Euclidean2d * p:V2d) -> V2d
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Transforms point p (p.w is presumed 1.0) by the inverse of the rigid transformation r. |
Multiply(a, b)
Signature: (a:Euclidean2d * b:Euclidean2d) -> Euclidean2d
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Multiplies 2 Euclidean transformations. This concatenates the two rigid transformations into a single one, first b is applied, then a. Attention: Multiplication is NOT commutative! |
Multiply(m, r)
Signature: (m:M22d * r:Euclidean2d) -> M23d
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op_Equality(r0, r1)
Signature: (r0:Euclidean2d * r1:Euclidean2d) -> bool
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op_Explicit(r)
Signature: r:Euclidean2d -> M23d
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op_Explicit(r)
Signature: r:Euclidean2d -> M33d
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op_Inequality(r0, r1)
Signature: (r0:Euclidean2d * r1:Euclidean2d) -> bool
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op_Multiply(a, b)
Signature: (a:Euclidean2d * b:Euclidean2d) -> Euclidean2d
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op_Multiply(m, r)
Signature: (m:M22d * r:Euclidean2d) -> M23d
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Parse(s)
Signature: s:string -> Euclidean2d
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TransformDir(r, v)
Signature: (r:Euclidean2d * v:V2d) -> V2d
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Transforms direction vector v (v.w is presumed 0.0) by rigid transformation r. Actually, only the rotation is used. |
TransformPos(r, p)
Signature: (r:Euclidean2d * p:V2d) -> V2d
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Transforms point p (p.w is presumed 1.0) by rigid transformation r. |
