# Questions tagged [geometric-transform]

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### How Can I Relax a Molecule in Mathematica?

I have a molecule in Mathematica. It consists of around 70 atoms, but let us for simplicity assume that we only have four atoms: ...
• 21
1 vote
99 views

### Bug in GeometricTransformation

Is this bug in newer versions of Mathematica still present? Cube is deformed with rotation angle being odd multiply of Pi/2. ...
• 20.1k
146 views

### How to efficiently duplicate and rotate a graphics object?

Consider the following code ...
• 4,903
1 vote
155 views

### How to rotate a 2-body system about various independent axes with body-fixed pivot points/rotation origins?

I am trying to simulate a jointed two-body system on Mathematica, consisting of these components: "Beam" and "Plate". I am constraining the system such that the beam is always ...
1 vote
101 views

### Metric tensor coordinate transformation with off-diagonal components

I know there is already an answer for this type of question given here: Computing the metric tensor under a coordinate transformation but the answer is not satisfactory as it is not clear to me how I ...
• 123
77 views

### Defining the rotation axis independent of the origin [closed]

I tried to rotate a 3D object in Graphics3D using GeometricTransformations with ...
48 views

### Show the translated version of a plot alongside another graphics object

I want to demonstrate the fact that the main part of a Mandelbrot fractal is consisted of a cardioid and some circles. So at first, I wrote this line: ...
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### Problem with FindGeometricTransform and NMinimize

I'm interested in Centroidal Voronoi tessellation. Here are two examples of unit disk tessellations: They are the same with respect to rotation. Recently, I've found ...
• 1,846
63 views

### Weird behaviour of TransformedRegion and GeometricTransformation

What I would like to do is to take some polyhedra (such as Cuboids, Prisms, and ...
• 221
113 views

### How to identify ellipses in grainy images and measure their position, semi-axes and orientation?

I am trying to analyze images of elliptical laser beams that are striking 'ground glass' surfaces. I need to determine the size, position and orientation of the ellipse that represents the boundary of ...
• 107
217 views

### Fill ParametricPlot3D into 3D solid shape

i have data point and transform it with matrix and plot with ParametricPlot3D and look like this my goals is to fill this and get the centroid with ...
• 157
56 views

### Combining two 3D objects

At this post How to combine one or more rotated graphics objects? There is a neat trick for combining 2D objects. When I apply it to 3D it does not work This code of a pyramid on a cube to approximate ...
• 940
93 views

### Distinguish the number of parameters of a function

I am looking to do a generalist job. For that I need to know the number of parameters. For now I'm using a true/false: ...
50 views

### oblique parallelepiped

I'm looking from a sketch of the 2D rectangle style, like this : Extrude[Rectangle[{1, 6}], Line[{{0}, {1}}]] But I want to extrude it in an oblique direction in ...
255 views

### Create a new graph based on a manipulated circle

I make a circle based on CirclePoints. From this list of points I take a part and rotate the coördinaties. Then I join the rotated part with the rest of the circelPoints. For example ...
• 2,855
1 vote
113 views

### Revolution of a 2D graphics

I would like to know how can we make a revolution around an axis of a 2D shape (a rectangle for example). I saw that there is the RevolutionPlot function but I can't manage to use it. I would also ...
76 views

### Material removal in a geometric shape

I want to do the same as in this program but drilling the rectangle in another direction, along an axis other than that of the cylinder : ...
1 vote
167 views

### Extruding a geometric shape along a path

I want to translate a 2D shape (a rectangle) along a path (a vector) in order to have a 3D shape, the same way extruding works in CAD software. In this answer, there is only a way to do it for a ...
75 views

### Fourier-Bros-Iagolnitzer transform

I would like to calculate the FBI transform of a set of Fourier series functions. The formula is: and here, $a$ and $n$ are integers, where $n=2$ since I have a 2-dimensional function to consider and ...
• 605
1 vote
34 views

### Applying a GeometricTransformation to an AxisObject along an InfiniteLine

I want to take a list of graphics primitives and draw them on top of another set of graphics primitives, using a child coordinate system. To do this, I'm using a ...
• 323
172 views

### Obtain coordinates from GeometricTransformation

What is the best way to obtain the transformed polygon coordinates? In the example below g3 still contains ...
• 31k
1 vote
60 views

### Transform a RegionFunction in ContourPlot3D problem

The (inspired) solution by @aardvark2012 to this original question: Transform a RegionFunction in ContourPlot3D worked well until an update appears to have changed the expected behavior (some time ...
• 1,391
116 views

### Mathematica generating 'incorrect' Cuboids

Mathematica 13.1 for some reason gives an error for the following code: ...
• 221
1 vote
35 views

### Numerical values versus exact values in GeometricTransformation

I have been doing some geometric transformations in 3D. The code bellow should transform (rotate) two black lines into red and blue tubes. At first I used exact values of coordinates and the result ...
• 20.1k
1 vote
32 views

### How to undo (cancel) manual rotations with GeometricTransformation

How to dynamically transform an object inside Graphis3D so that when whole Graphis3D is manually rotated by pointer the object ...
• 20.1k
84 views

### Code to do geometric transformation equivalent to dragging by mouse in circle

We can click and drag Graphics3D objects. Suppose you click and drag on such an object in the center of it and move your pointer of mouse in a circle of radius <...
• 20.1k
57 views

### Is it possible to extract geometric transforms from ImageStitch (Mathematica 13)?

Is there a way to extract the Method settings and/or geometric transforms that ImageStitch[] (Mathematica 13) uses to compose a list of images? I have ~40 digital microscope image frames along with ...
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96 views

### How to "restart" AnglePath3D[]?

Suppose we start a random path in 3D, stopping at the $5^{th}$ step. Importantly, we make a new random orientation at every new step. ...
• 1,613
254 views

### How to project a 2D region from one plane to another?

I have one of a general set of 2D regions (Disk, Rectangle, Polygon, etc.), as well as 3D origin points and normal vectors defining two reference planes/coordinate systems. I want to find a series of ...
174 views

### Strange behaviour in GeometricTransformation

Bug introduced in 13.0 **Bug is fixed in Version 13.1 ** I came across the following strange behaviour with the GeometricTransformation function. ...
• 4,083
69 views

### Replicate atomic coordinates in x, y direction [closed]

I have x and y coordinates of a lattice. I want to replicate the system in x and y directions. Can you please guide me on this.
• 7
1 vote
177 views

### How to linear transform an equation?

I want to scale transform the equation (not the graph) of a circle. Specifically, I want to scale 4x by the x-axis and 3x by the y-axis. I use the following ...
• 49
175 views

### Transform a region using the flow of differential equation

I was looking to apply a nonlinear transformation to a geometric region, say a rectangle to obtain a transformed region. According to the documentation for TransformedRegion, one requires a Region and ...
• 159
121 views

### FindRegionTransform again

Bug introduced in 13.0.0 [CASE:4895492] [CASE:4895697] Studying a new command of version 13.0.0 FindRegionTransform, I execute an example from the documentation: <...
• 27.3k
1 vote
63 views

### Possible bug in FindRegionTransform

Studying a new command FindRegionTransform of version 13.0.0 on Windows 10, I try to reproduce an example from the documentation , but obtain a different result <...
• 27.3k
1 vote
126 views

### Obtain angles of rotation from singular vectors U and V from SVD

My question is a continuation to a previous question. I have a matrix M which is a function of theta1, theta2, phi1 and phi2. Now, I want to get back these angles using the singular vectors (U and V) ...
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95 views

### Normal not working with Translate and some Graphics object [duplicate]

in v13, Normal doesn't seem to work with Translate and some Graphics objects like Rectangle ...
• 15.2k
82 views

I hope someone can assist me as I am pretty new to Mathematica and understanding the language is a bit of a hurdle. I am trying to rotate a plot of interlaced circles by some angle without rotating ...
77 views

### 3D shearing w. r. t. x-axis [closed]

Shearing in $X$ axis is achieved by using the following shearing equations- X_new = X_old, Y_new = Y_old + Sh_y × X_old, Z_new = Z_old + Sh_z × X_old My question is during Y_new and Z_new calculations ...
• 99
1 vote
178 views

### How to use VectorAngle[] in AnglePath3D[]?

Suppose I have a specific angle that I calculate from two vectors, in 3D: ...
• 1,613
170 views

### How to align two ellipsoids along center and long axes?

I'm struggling to understand rotation/translation transforms as applied to things like spheres and ellipsoids. Take the following silly example. Given this pair of random ellipsoids, how do I find a ...
• 1,613
1 vote
161 views

### Transfer distribution of points on a sphere to an Ellipsoid[]?

I've seen this cool function, which generates a given distribution of points on the unit sphere, known as Dimroth-Watson distribution: ...
• 1,613
109 views

### On the geometric transformations of polygons

Each starry set has the following property: ...
• 335
1 vote
157 views

### Image Perspective Transformations

I'm trying to detect the license plate in these types of images which may be captured from various perspectives and lighting I've found it easiest to detect these two points corresponding to the ...
• 829
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### Hyperbolic tiling of 3d objects

I have created a 3d object using plot3d and want to try and tile it hyperbolicly. It has a hexagonal cross section and it's the hexagons that I want to tile. Is there a way I can take an object and ...
• 183
92 views

### How to apply GeometricTransformation to ArrayPlot?

In a previous version of Mathematica (maybe version 7), it was possible to use GeometricTransformation on an ArrayPlot. That ...
• 21
182 views

### Sweep, scale, and rotate implicit 3d region or contour plot along an arbitrary curve

Suppose I have a 3d region or contour that is implicitly defined and has no explicit parameterization. This is easy to plot, as RegionPlot3D and ContourPlot3D allow implicit functions. But now I want ...
• 121
548 views

### Is it possible to directly translate or rotate a Graphics or Graphics3D object?

I have seen the documentation for Translate (https://reference.wolfram.com/language/ref/Translate.html), which allows one to translate a graphics primitive (like <...
• 553
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### Distorting image to ensure consistent vanishing point

Here's Giorgio de Chirico's painting, Ariadne: The Surrealist artist deliberately broke the rules of geometric perspective, giving the work his characteristic sense of mystery and unease. What would ...
• 41.8k
I need to generate a random rotation matrix for a given angle $a$. In other words, a random $n\times n$ matrix $A$ such that for any unit-length vector $v$ the following is true. $$v'Av\le\cos a$$ The ...