# Moving a parametric object in mathematica

• Mathematica
• andlook
In summary, to move a parametrically defined 3D object, you can use the GeometricTransformation function with the Graphics3D object and a matrix defining the transformation. Just make sure to access the Graphics3D primitive using obj[[1]] and any options using obj[[2]].
andlook
Hi

I have define a 3D object with ParametricPlot3D, something similar to a sphere called "obj." I then want to use a matrix, I define as "move," to translate the object around, I have been trying:

obj = ParametricPlot3D...
move = AffineTransform[{{1, 1, 2}, {0,1 , 1}, {0, 0, 1}}]

Graphics3D[GeometricTransformation[obj[], move], Axes -> True]

But this just returns an error message
"GeometricTransformation is not a Graphics3D primitive or directive." Is it possible to move an object that has been defined parametrically like this? Is there any other command that will allow me to move this object around?

Thanks

The result of ParametricPlot3D is a Graphics3D object, not a Graphics3D primitive. However, it should have a length of 2 and the first element should be a list of the corresponding Graphics3D primitive and the second element should be a list of the options. So you can use something like:

Graphics3D[GeometricTransformation[obj[[1]], move]]
or even
Graphics3D[GeometricTransformation[obj[[1]], move], obj[[2]]]

for your question. Yes, it is possible to move a parametric object in Mathematica using GeometricTransformation. However, the syntax you have used is incorrect. The correct syntax would be:

obj = ParametricPlot3D[...];
move = AffineTransform[{{1, 1, 2}, {0, 1, 1}, {0, 0, 1}}];

Graphics3D[GeometricTransformation[obj[[1]], move], Axes -> True]

The key difference is that you need to access the actual graphics object within the ParametricPlot3D using [[1]]. Additionally, the affine transformation matrix should be applied to the graphics object, not the ParametricPlot3D function itself.

I hope this helps and you are able to successfully move your parametric object. If you continue to have trouble, I suggest consulting the Mathematica documentation or seeking help from the Mathematica community forums. Good luck with your project!

## 1. How do I move a parametric object in Mathematica?

To move a parametric object in Mathematica, you can use the Translate function. This function takes in the parametric object as its first argument and the desired translation vector as its second argument.

## 2. Can I specify the direction and distance of the movement?

Yes, you can specify both the direction and distance of the movement using the Translate function. The second argument of the function is a vector, where the direction of the vector determines the direction of the movement and the magnitude of the vector determines the distance of the movement.

## 3. How do I rotate a parametric object in Mathematica?

To rotate a parametric object in Mathematica, you can use the Rotate function. This function takes in the parametric object as its first argument and the desired rotation angle in radians as its second argument.

## 4. Is it possible to combine translation and rotation to move a parametric object in a specific path?

Yes, you can combine translation and rotation using the TransformedRegion function. This function allows you to apply multiple transformations to a parametric object in a specific order.

## 5. Can I animate the movement of a parametric object in Mathematica?

Yes, you can use the Animate function to create an animation of the movement of a parametric object. This function takes in the parametric object and the desired range of movement as its arguments.

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