Programs: off_trans 14 images tree :: Antiprism Examples and Visual Reference > Program Examples > Programs: off_trans
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Example commands using the off_trans program. This program applies Euclidean transformations (rotations, translations, reflections, central inversion), and scaling transformations to the model. Some transformations are specified using the coordinate system alone (e.g. a translation of 2 units in the direction of the z-axis) while others also reference the model being transformed (e.g. a translation that carries the model centroid onto the coordinate origin).

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Translate  Med    Lrg
 Description : The -T option specifies a translation. The argument is three values for the number of units to translate the model along the x, y and z axes. In this example the model is translated 0.5 units in the direction of the x-axis, 0.2 in the direction of the y-axis and 0.1 in the direction of the z-axis. View this model with the command `off_color -r A0.2,f ant4 > orig.offoff_trans -T 0.5,0.2,0.1 ant4 | antiview -C 0,0,0 - orig.off`

Rotate 3 O  Med    Lrg
 Description : The -R option specifies a rotation about the origin. If the argument is three values, these are the number of degrees to rotate the model around the x, y and z axes, in that order. In this example the model is rotated -30 degrees around the x-axis. View this model with the command `off_color -r A0.2,f ant4 > orig.offoff_trans -R -30,0,0 ant4 | antiview -C 0,0,0 - orig.off`

Rotate 3 O  Med    Lrg
 Description : The -R option specifies a rotation about the origin. If the argument is three values, these are the number of degrees to rotate the model around the x, y and z axes, in that order. In this example the model is rotated 90 degrees around the x-axis, then 30 degrees around the z-axis. View this model with the command `off_color -r A0.2,f ant4 > orig.offoff_trans -R 90,0,30 ant4 | antiview -C 0,0,0 - orig.off`

Rotate 4 O  Med    Lrg
 Description : The -R option specifies a rotation about the origin. If the argument is four values this is a rotation about a single axis. The first three values are a vector giving the direction of the axis, the fourth value is the number of degrees to rotate. In this example the model is rotated 30 degrees around the y-axis. View this model with the command `off_color -r A0.2,f ant4 > orig.offoff_trans -R 0,1,0,30 ant4 | antiview -C 0,0,0 - orig.off`

Rotate 4 O  Med    Lrg
 Description : The -R option specifies a rotation about the origin. If the argument is four values this is a rotation about a single axis. The first three values are a vector giving the direction of the axis, the fourth value is the number of degrees to rotate. In this example the model is rotated 30 degrees around an axis in the direction (1, 1, 0); halfway between the x and y axes. View this model with the command `off_color -r A0.2,f ant4 > orig.offoff_trans -R 1,1,0,30 ant4 | antiview -C 0,0,0 - orig.off`

Rotate 6 O  Med    Lrg
 Description : The -R option specifies a rotation about the origin. If the argument is six values this is a rotation of a 'from' vector (the first three numbers) onto a 'to' vector (the second set of three numbers) about a axis perpendicular to the two vectors. In this example aligning a vertex of a cube with the z-axis the rotations does not nicely align the cube with the x and y axes, for that see the 12 parameter rotation. View this model with the command `off_trans -R 1,1,1,0,0,1 cube | antiview`

Rotate 12 O  Med    Lrg
 Description : The -R option specifies a rotation about the origin. If the argument is 12 values this is a rotation that carries two 'from' vectors (the first and second set of three numbers), onto two 'to' vectors (the third and fourth set of three numbers). It may not be possible to align the second 'from' vector with the second 'to' vector, in which case the second 'from' vector will be carried to lie in the plane of the two 'to' vectors. In this example the cube has a vertex aligned with the z-axis, and a second vertex aligned in the zx-plane. View this model with the command `off_trans -R 1,1,1,1,1,-1,0,0,1,1,0,0 cube | antiview`

Rotate 3 Pt  Med    Lrg
 Description : The -R option specifies a rotation about the origin. To rotate about a point that isn't the origin: translate by the negative of the coordinates of the point, then rotate, then translate by coordinates of the point. In this example the model is rotated about an axis through the point (1,0,0). View this model with the command `off_color -r A0.2,f ant4 > orig.offoff_trans -T -1,0,0 -R 0,0.01,-10 -T 1,0,0 ant4 | antiview -C 0,0,0 - orig.off`

Scale 1 O  Med    Lrg
 Description : The -S otion specifies a scaling, while fixing the origin. If the argument is one value the scaling will be by this value in all directions. View this model with the command `off_color -r A0.2,f ant4 > orig.offoff_trans -S 0.8 ant4 | antiview -C 0,0,0 - orig.off`

Scale 3 O  Med    Lrg
 Description : The -S otion specifies a scaling, while fixing the origin. If the argument is three values these are the factors to scale in the x, y and z directions. View this model with the command `off_color -r A0.2,f ant4 > orig.offoff_trans -S 1.5,0.7,0.5 ant4 | antiview -C 0,0,0 - orig.off`

Mirror 3 O  Med    Lrg
 Description : The -M option specifies a reflection in a plane passing through the origin. The argument is three values, which specify a vector normal to the plane. View this model with the command `off_color -r A0.2,f ant4 > orig.offoff_trans -M 1,0,0.0001 ant4 | antiview -C 0,0,0 - orig.off`

Mirror 3 Pt  Med    Lrg
 Description : The -M option specifies a reflection in a plane passing through the origin. To reflect in a plane that doesn't pass through the origin: translate by the negative of the coordinates of a point on the plane, then mirror in the required direction, then translate by the coordinates of the point. In this example the model is reflected in a plane through the point (0.2,0,0). View this model with the command `off_color -r A0.2,f ant4 > orig.offoff_trans -T -0.2,0,0 -M 1,0,0.0001 -T 0.2,0,0 ant4 | antiview -C 0,0,0 - orig.off`

Inversion O  Med    Lrg
 Description : The -I option specifies reflection, or inversion, in the origin. It turns coordinates into their negatives. View this model with the command `off_color -r A0.2,f J33 > orig.offoff_trans -I J33 | antiview -C 0,0,0 - orig.off`

Inversion Pt  Med    Lrg
 Description : The -I option specifies reflection, or inversion, in the origin. To produce a reflection (inversion) in a point other than the origin: translate by the negative of the coordinates of the point, then reflect in the origin, then translate by the coordinates of the point. In this example the model is reflected in the point (0.2,0,0). View this model with the command `off_color -r A0.2,f J33 > orig.offoff_trans -T -0.2,0,0 -I -T 0.2,0,0 J33 | antiview -C 0,0,0 - orig.off`