CompoundMatrixArithmetic¶

MacroModule¶

genre	`File`
author	`Darko Ojdanic`
package	`FMEwork/ReleaseMeVis`
definition	CompoundMatrixArithmetic.def
see also	`MatrixArithmetic`, `DecomposeMatrix`, `ComposeMatrix`
keywords	`matrix`, `matrices`, `arithmetic`, `multiplication`, `compound`, `homogeneous`, `affine`, `transformation`, `inverse`

Purpose¶

Calculation of arithmetic expressions for several 4x4 matrices.

Usage¶

Write the expression in the typical form like this:

A*B*trans(C)*inv(D) + A*s1 - B*3.4

The module can calculate two expressions (P and Q), where the result of the first expression can be used for the second one. Multiplication of a matrix with a column vector is also possible. There are 8 matrices (A,B,…H) that may be used as an input for the calculation, 4 scalars (s1,..,s4) and two vector (v1,v2).

Details¶

Available operations:

Operation Name	Function
Add	A + B
Subtract	A - B
Multiply	A * B
Add scalar	A + s1
Multiply with scalar	A * s1
Multiply with vector	A * v1
Inverse	inv(A)
Transpose	trans(A)
Identity matrix	eye(A)
Negate	-A
Inverse of transformation matrix	inv_t(A)

A special inverse function is implemented for the homogeneous transformation matrices used for 3D rotations and translations, inv_t(A). If the matrix is represented as:

../../../Modules/Macros/CompoundMatrixArithmetic/mhelp/Images/T.jpg

the inverse is calculated as:

../../../Modules/Macros/CompoundMatrixArithmetic/mhelp/Images/invT.jpg

where p, n, o, a are column vectors of the matrix T, and “dot” represents scalar product.

The multiplication with the vector (e.g., A*v1) is only allowed for the column vectors, i.e., right side multiplication. Output vectors vp and vp hold the result in that case.

Scalar math functions like sqrt(),cos(),sin(), acos(), etc. or constant “pi” can be also used, as well as all other functions from the python math library. For example like this:

A*C + B*cos(pi/3)

If a pure scalar expression is given, the result appears in the corresponding output fields (sp or sq). On an empty expression, the result is the identity matrix.

Interaction¶

The output is updated whenever changes occur to the matrix or scalar inputs, or the field for the arithmetic expression.

Tips¶

The example network demonstrate a simple translation of a contour.

If you write an input matrix which is not 4x4, but for example an 5x5 matrix, no error will be reported; the result will be calculated with the first 16 elements (read as a string). So be careful, use only 4x4 matrix!

Windows¶

Default Panel¶

../../../Modules/Macros/CompoundMatrixArithmetic/mhelp/Images/Screenshots/CompoundMatrixArithmetic._default.png

Parameter Fields¶

Field Index¶

`Calculate (calcP)`: `Trigger`	`First expression (P)`: `String`	`resVectorQValid`: `Bool`
`Calculate (calcQ)`: `Trigger`	`Matrix A`: `Matrix`	`s1`: `Float`
`Comment (expPComment)`: `String`	`Matrix B`: `Matrix`	`s2`: `Float`
`Comment (expQComment)`: `String`	`Matrix C`: `Matrix`	`s3`: `Float`
`Comment (matrixAComment)`: `String`	`Matrix D`: `Matrix`	`s4`: `Float`
`Comment (matrixBComment)`: `String`	`Matrix E`: `Matrix`	`Second expression (Q)`: `String`
`Comment (matrixCComment)`: `String`	`Matrix F`: `Matrix`	`sp`: `Float`
`Comment (matrixDComment)`: `String`	`Matrix G`: `Matrix`	`sq`: `Float`
`Comment (matrixEComment)`: `String`	`Matrix H`: `Matrix`	`v1`: `Vector4`
`Comment (matrixFComment)`: `String`	`Matrix P`: `Matrix`	`v2`: `Vector4`
`Comment (matrixGComment)`: `String`	`Matrix Q`: `Matrix`	`vp`: `Vector4`
`Comment (matrixHComment)`: `String`	`resScalarPValid`: `Bool`	`vq`: `Vector4`
`Comment (scalarsComment)`: `String`	`resScalarQValid`: `Bool`
`Comment (vectorsComment)`: `String`	`resVectorPValid`: `Bool`

Visible Fields¶

First expression (P)¶

name: expressionP, type: String¶: For example A*B*trans(C)*inv(D)

Second expression (Q)¶

name: expressionQ, type: String¶: For example A*B*trans(C)*inv(D)*P

Comment (expPComment)¶

name: expPComment, type: String¶: Description of expression P

Comment (expQComment)¶

name: expQComment, type: String¶: Description of expression Q

Matrix A¶

name: matrixA, type: Matrix, default: 0 0 0 0, 0 0 0 0, 0 0 0 0, 0 0 0 0¶: Provide a 4x4 matrix

Matrix B¶

name: matrixB, type: Matrix, default: 0 0 0 0, 0 0 0 0, 0 0 0 0, 0 0 0 0¶: Provide a 4x4 matrix

Matrix C¶

name: matrixC, type: Matrix, default: 0 0 0 0, 0 0 0 0, 0 0 0 0, 0 0 0 0¶: Provide a 4x4 matrix

Matrix D¶

name: matrixD, type: Matrix, default: 0 0 0 0, 0 0 0 0, 0 0 0 0, 0 0 0 0¶: Provide a 4x4 matrix

Matrix E¶

name: matrixE, type: Matrix, default: 0 0 0 0, 0 0 0 0, 0 0 0 0, 0 0 0 0¶: Provide a 4x4 matrix

Matrix F¶

name: matrixF, type: Matrix, default: 0 0 0 0, 0 0 0 0, 0 0 0 0, 0 0 0 0¶: Provide a 4x4 matrix

Matrix G¶

name: matrixG, type: Matrix, default: 0 0 0 0, 0 0 0 0, 0 0 0 0, 0 0 0 0¶: Provide a 4x4 matrix

Matrix H¶

name: matrixH, type: Matrix, default: 0 0 0 0, 0 0 0 0, 0 0 0 0, 0 0 0 0¶: Provide a 4x4 matrix

Matrix P¶

name: matrixP, type: Matrix, default: 1 0 0 0, 0 1 0 0, 0 0 1 0, 0 0 0 1¶: Result of the expression P, if the result is a matrix - otherwise a unit matrix is given.

Matrix Q¶

name: matrixQ, type: Matrix, default: 1 0 0 0, 0 1 0 0, 0 0 1 0, 0 0 0 1¶: Result of the expression Q, if the result is a matrix - otherwise a unit matrix is given.

Comment (matrixAComment)¶

name: matrixAComment, type: String¶: Description of matrix A

Comment (matrixBComment)¶

name: matrixBComment, type: String¶: Description of matrix B

Comment (matrixCComment)¶

name: matrixCComment, type: String¶: Description of matrix C

Comment (matrixDComment)¶

name: matrixDComment, type: String¶: Description of matrix C

Comment (matrixEComment)¶

name: matrixEComment, type: String¶: Description of matrix E

Comment (matrixFComment)¶

name: matrixFComment, type: String¶: Description of matrix F

Comment (matrixGComment)¶

name: matrixGComment, type: String¶: Description of matrix G

Comment (matrixHComment)¶

name: matrixHComment, type: String¶: Description of matrix H

Comment (scalarsComment)¶

name: scalarsComment, type: String¶: Description of scalars

Comment (vectorsComment)¶

name: vectorsComment, type: String¶: Description of vectors

s1¶

name: s1, type: Float, default: 0¶

s2¶

name: s2, type: Float, default: 0¶

s3¶

name: s3, type: Float, default: 0¶

s4¶

name: s4, type: Float, default: 0¶

Calculate (calcP)¶

name: calcP, type: Trigger¶

Calculate (calcQ)¶

name: calcQ, type: Trigger¶

sp¶

name: sp, type: Float, default: 0¶: Result of the expression P, if the result is a scalar - otherwise zero.

sq¶

name: sq, type: Float, default: 0¶: Result of the expression Q, if the result is a scalar - otherwise zero.

v1¶

name: v1, type: Vector4, default: 0 0 0 0¶: Provide an input vector

v2¶

name: v2, type: Vector4, default: 0 0 0 0¶: Provide an input vector

vp¶

name: vp, type: Vector4, default: 0 0 0 1¶: Result of the expression P, if the result is a vector - otherwise (0,0,0,1) is given.

vq¶

name: vq, type: Vector4, default: 0 0 0 1¶: Result of the expression Q, if the result is a vector - otherwise (0,0,0,1) is given.

Hidden Fields¶

resScalarPValid¶

name: resScalarPValid, type: Bool, default: FALSE¶

resVectorPValid¶

name: resVectorPValid, type: Bool, default: FALSE¶

resScalarQValid¶

name: resScalarQValid, type: Bool, default: FALSE¶

resVectorQValid¶

name: resVectorQValid, type: Bool, default: FALSE¶