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wszst matrix

Use the transformation options as base and calculate and print the related vectors and the transformation matrices. Then do a forward and backward transformation for each vector parameter using the matrices and print the results. The transformations are done with 4 different methods to confirm the algorithms. Only the main results and results, which differ, are printed.

Normally, the exit status is OK (null). If at least one old transformation returns different results for the different algorithms, then status DIFFER (not null) is returned.

Contents

1.   Syntax

wszst MATRIX [patch-option]... [vector]...

2.   Options

Options
Option Param Description
-c --const list Define constant values, that are used by the internal encoders and by the numeric options as predefined global variables. This option allows a conditional encoding of text files. It can be used multiple times for multiple definitions.

The Parameter is a comma separated list of terms and a term is 'name=expression'. The expression is calculated by the text parser.

--scale vector[@origin] Transform the data: Scale all coordinates and size values by 'vector' relative to the point 'origin'. If the origin is not set, 0,0,0 is used instead.

Negative values mirror the coordinates. Each parameter is either a vector expression or a comma separated expression list of coordinates ('x,z' or 'x,y,z').

Transformations are calculated in the order SCALE, SHIFT, ROTATE, TRANSLATE.

--shift vector Transform the data: Add 'vector' to all coordinates. Is's simlar to --translate, but the addition is done before rotation. The parameter is either a vector expression or a comma separated expression list of coordinates ('x,z' or 'x,y,z').

Transformations are calculated in the order SCALE, SHIFT, ROTATE, TRANSLATE.

--xss x1old,x1new,x2old,x2new --xss (x-scale-shift) calculates the X values of --scale and --shift, so that the old values are transformed to the new values. The parameters are numbers or expression.
--yss y1old,y1new,y2old,y2new --yss (y-scale-shift) calculates the Y values of --scale and --shift, so that the old values are transformed to the new values. The parameters are numbers or expression.
--zss z1old,z1new,z2old,z2new --zss (z-scale-shift) calculates the Z values of --scale and --shift, so that the old values are transformed to the new values. The parameters are numbers or expression.
--rot degree[@origin] Transform the data: Rotate all coordinates and rotation values by the angle 'degree' (is a vecotr) around the 3 axes. All 3 axes goes through the point 'origin'. If the origin is not set, 0,0,0 is used instead.

Each parameter is either a vector expression or a comma separated expression list of coordinates ('x,y,z').

Option --rot is an alternative for --xrot, --yrot and --zrot to define all 3 rotations in one step. Transformations are calculated in the order SCALE, SHIFT, X-ROTATE, Y-ROTATE, Z-ROTATE, TRANSLATE.

--xrot degree[@origin] Transform the data: Rotate all coordinates and rotation values by the angle 'degree' around the x-axis, that goes through the point 'origin'. If the origin is not set, 0,0,0 is used instead.

Each parameter is either a vector expression or a comma separated expression list of coordinates ('y,z' or 'x,y,z').

Transformations are calculated in the order SCALE, SHIFT, X-ROTATE, Y-ROTATE, Z-ROTATE, TRANSLATE.

--yrot degree[@origin] Transform the data: Rotate all coordinates and rotation values by the angle 'degree' around the x-axis, that goes through the point 'origin'. If the origin is not set, 0,0,0 is used instead. This is a horizontal counterclockwise rotation and the old option name --hrot can also used.

Each parameter is either a vector expression or a comma separated expression list of coordinates ('x,z' or 'x,y,z').

Transformations are calculated in the order SCALE, SHIFT, X-ROTATE, Y-ROTATE, Z-ROTATE, TRANSLATE.

--zrot degree[@origin] Transform the data: Rotate all coordinates and rotation values by the angle 'degree' around the z-axis, that goes through the point 'origin'. If the origin is not set, 0,0,0 is used instead.

Each parameter is either a vector expression or a comma separated expression list of coordinates ('x,y' or 'x,y,z').

Transformations are calculated in the order SCALE, SHIFT, X-ROTATE, Y-ROTATE, Z-ROTATE, TRANSLATE.

--ypos pos This option defines an Y position for KMP/CKPT transformations. It has only impact to X and Z rotations (Options --xrot and --zrot). If not set, the mean y of the active rotation origins are used.
--translate vector Transform the data: Add 'vector' to all coordinates. Is's simlar to --shift, but the addition is done after rotation. The parameter is either a vector expression or a comma separated expression list of coordinates ('x,z' or 'x,y,z'). --trans is a short cut.

Transformations are calculated in the order SCALE, SHIFT, ROTATE, TRANSLATE.

--null Create a neutral transformation without affecting the coordinates. The only influence is, that the dependent values (like maximum) are re-calculated as if a transformation has taken place.
--next Close the current transformation step with all scaling, shifting, rotation and translation options and open a new step with cleared options. On transformation each step is logical done one by one. In real, one total transformation matrix is calculated and used for fast transformations.

If option --next is used, the ability for modifying the scale and rotation vectors (not the positions) of different KMP sections is nearly always lost. A warning is printed if this occurs.

--ascale factor@dir Transform the data and do an axis scale: Close the current transformation step like --next and scale the data by 'factor' into the direction given by the vector 'dir'. Store the resulting matrix as single transformation step and open a new one.

This kind of transformation is EXPERIMENTAL!

--arot degree[@pos1]@pos2 Transform the data and do an axis rotation: Close the current transformation step like --next and rotate the data by 'degree' around the axis defined by the 2 points. If 'pos1' is not set, use 0,0,0 instead. Store the resulting matrix as single transformation step and open a new one.

This kind of transformation is EXPERIMENTAL!

--tform-script script Load the script and execute it by the text parser.

Then for each coordinate (2D and 3D), call the macro TRANSFORM after all other transformations. Call it without parameters and set variable $I with a zero based index of all vertices, variable $D to the dimension (2 or 3) and the variable $P to the vector of the current vertex. If the macro returns a vector, it is the new position.

For each file, macro BEGIN is called at the beginning and END after proccessing all points, but only, if the macros are defined. For END, variable $I is set to the number of proccessed vertices in the current file.

Before each macro call, the private and local variables are cleared and only global parameters are permanent. The zero based index is cleared for each new source. The parameters of the macro calls are defined in the local name space.

-B --brief If set once, suppress vector dumps for transformation steps and ignore option --long. If set twice, suppress vector dump for final transformation too.
-l --long If set once, print inverse matrix for the final transformation. If set twice, print inverse matrix for all transformations.
-q --quiet Option --quiet is dedicated to automatic tests comparing the old and new transformation algorithms. If set once, the tables are only printed, if the results differ. If set twice, nothing is printed at all and only the exit status will inform about the results.

3.   Description

The matrix command helps to analyze the scanning of transformation options. First it prints a list of the internal representation of the scanned options. If 2 or more transformation steps are defined, each step and also the final transformation matrix is printed.

Then it reads each parameter and scan it as a vector position. The position is transformed in different ways to confirm the algorithms.