# Questions tagged [geometric-transform]

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### Mathematica generating 'incorrect' Cuboids

Mathematica 13.1 for some reason gives an error for the following code: ...
• 203
1 vote
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### 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 ...
• 3,735
1 vote
27 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 ...
• 3,735
63 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 <...
• 3,735
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### 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 ...
• 91
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### 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. ...
• 1,563
83 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 ...
115 views

### Strange behaviour in GeometricTransformation

Bug introduced in 13.0 I came across the following strange behaviour with the GeometricTransformation function. ...
• 3,616
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### Replicate atomic coordinates in x, y direction

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.
• 1
1 vote
156 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 ...
• 39
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### 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 ...
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### 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: <...
• 18.3k
1 vote
61 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 <...
• 18.3k
1 vote
67 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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### 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 ...
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### Can someone please help me in breaking down what this code means?

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 ...
69 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
151 views

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

Suppose I have a specific angle that I calculate from two vectors, in 3D: ...
• 1,563
119 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 ...
• 1,563
1 vote
109 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: ...
• 1,563
83 views

### On the geometric transformations of polygons

Each starry set has the following property: ...
• 191
1 vote
88 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 ...
• 819
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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 ...
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### 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
112 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
1 vote
196 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 <...
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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 ...
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259 views

### Random rotation at a given angle?

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 ...
• 6,441
167 views

### FindGeometricTransform not working properly for a simple problem

I am surprised why FindGeometricTransform is failing to automatically register or align two sets of points that are drawn from a ...
• 8,598
116 views

### Nest or fold a series of geometric transforms

I have a requirement to perform a series of GeometricTransformation[]s using the AfineTransform[] function. I use these to set ...
• 187
112 views

### EulerMatrix with axes other than X, Y an Z

The Mathematica function EulerMatrix[{Alpha, Beta, Gamma},{a,b,c}] gives the Euler matrix for rotation about X, Y and Z axes. Here by choosing the order of a, b and ...
• 1,003
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### Affine transform of sparse list (x,y,z) to a region of x^2 + y^2 + z^2 = 1.0

I have list of x,y,z points (somewhat random) that leads to the image shown below: I am trying to map this data to essentially a sphere shape using an affine transform. My original attempt was to ...
1 vote
153 views

### Visualizing an Affine Matrix

I have a computer graphics program that prints out affine matrices like ...
• 2,995
1 vote
102 views

### How to modify a particular step length in a 3D random walk?

Suppose I simulate a random walk in 3D using AnglePath3D[]: ...
• 1,563
34 views

### How to reorient a Sphere[] and associated point based on some arbitrary axis?

Suppose I have a unit Sphere[] sitting at the center {0,0,0}, with a point on its "north pole", like this one: ...
• 1,563
197 views

### How to extrude a tapered shape (starting from a previous answer)

I have a shape given by ...
• 2,005
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### Find nearest crop of image within another image

ImageAlign[ref, i] works well when image i is fully contained within the reference image ref,...
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### Need help understanding Graphics Translate

I created a star pattern that I was trying to apply to a circle of pentagons, but the Translate had a slight offset, and I don't understand why. When I drew the ...
• 303
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### Region function of rotated Polyhedron

Is it possible to find the equation of the internal region of a rotated polyhedron? For example, the analytic region for a Dodecahedron is found by: ...
• 549
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### Why can't an annulus be mapped as a rectangle

The following code is used to map an annulus to a rectangle: ...
719 views

### How to visualize a spherical mesh on a squared plane?

I need to visualize the points of a spherical mesh on a squared plane (this question is different than this one, I believe). For instance, let us first generate points ...
• 1,563
77 views

### Setting the location of the origin within an image for AffineTransformation

This question is closely related to this one, but slightly different. I want to perform several AffineTransforms on an image (myImage). For example, here is a ...
• 36.7k
105 views

### Geometric transform of a plot with legends and title

I'm doing a ternary phase diagram, so I want to plot it in a triangle and not in a square. If I'm doing the transformation with legends it doesn't work, but if I don't put legends it does work. Why ...
• 1,235
219 views

### Transforming 2D points on to a regular grid or lattice

I have a set of points in 2D generated by doing a DimensionReduce on a list of colors: ...
• 625
1 vote
108 views

### Apply non-linear transformation to graphics object

I would like to define some simple geometric primitives (e.g. points and lines) and see what happens when I transform them by a non-linear transformation (in my case $(x,y)\mapsto (\sqrt x,\sqrt y)$). ...
1 vote
90 views

### Translate (and scale) AnatomyData in three-dimensions

I would like to create a Graphics3D entity consisting of a human eyeball and a complex figure defined elsewhere. (For a minimal working example, assume that the ...
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