# Questions tagged [geometric-transform]

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### 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 ...
51 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 ...
98 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 ...
62 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 ...
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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 ...
69 views

### Visualizing an Affine Matrix

I have a computer graphics program that prints out affine matrices like ...
58 views

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

Suppose I simulate a random walk in 3D using AnglePath3D[]: ...
27 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: ...
124 views

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

I have a shape given by ...
98 views

### Find nearest crop of image within another image

ImageAlign[ref, i] works well when image i is fully contained within the reference image ref,...
14 views

### How to concatenate multiple CapsuleShape[] while changing their size?

I am trying to create a 'chain' of capsules so that they are concatenated at certain points. Then, I want to change the size (radius, etc) of a given capsule, while preserving the relative orientation ...
64 views

### 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 ...
83 views

### 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: ...
211 views

### Why can't an annulus be mapped as a rectangle

The following code is used to map an annulus to a rectangle: ...
605 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 ...
33 views

### How to get the transformation function from one plane to another?

Suppose I have a plane which passes through some point $(x_0,y_0,z_0)$ and has a (normalized) surface normal $n$. Consider as an example a plane that passes through the point ...
41 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 ...
69 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 ...
216 views

### How do you implement metric tensor in Mathematica?

I'm trying to follow several tutorials on metric tensors. One of the common exercises is a polar metric. I'm stuck trying to implement this in Mathematica. According to the derivation, the polar ...
151 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: ...
63 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 $(x,y)\mapsto (\sqrt x,\sqrt y)$). ...
71 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 ...
79 views

240 views

### Rotating panels with GeometricTransformation

In the field of architecture, learning to manipulate geometry so comprehensively with Mathematica has been fun. However, I seem to have reached my limits with the following ...
958 views

### How to double (or triple) each element of equation?

x^2/3+y^2/9==1 (0.5x)^2/3+(0.5*y)^2/9==1 Looks at above two equation,I multiply 0.5 to each element of second equation,which means when plotting, each point ...
402 views

### rotate image around fixed point

How can I painlessly rotate a tiff image by some small angle around a point with specific coordinates? The image shouldn't be altered otherwise, it can be padded with zeros if necessary, and then ...
458 views

### How to transform general Ellipsoid into rotated axis-oriented one?

Recently, I discovered a long-standing bug in the rendering of Disk and Circle primitives after applying ...
236 views

### Why BoundingRegion does not work well?

Bug introduced in 8 or earlier and fixed in 12.0.0 The underlying bug is unstable and wrong rendering of Disk[] and Circle[] ...
344 views

### How to determine roll pitch and yaw/Euler angles from approximately orthogonal matrix?

I have a collection of rigid bodies, each comprising ~100 particles. Each body is defined by a list of points corresponding to the coordinates of its constituent particles. The rigid bodies are ...
60 views

### How to get explicit result of geometric transformation? [duplicate]

Seems like this simply rectangle rescale should work and return the exact coordinates of the transformed resulting rectangle (which should be ...
513 views

### Extracting data from analog screen photograph

I'm using an analog profilometer from the 1970s and need a way to digitize the data and the only way is through a photograph. I've searched but all I could find was how to extract data from computer ...
152 views

### Rotate a RegionPlot3D

I plotted a bunch of regions using RegionPlot3D, and would need to rotate them around an a vector {0,0,1} anchored at point {5,5,5}. I tried RotationTransform, Transformed Region, and changing ...
167 views

### Performing geometric transforms on 3D text inside a Graphics3D expression

I am trying to put some 3D text inside a 3D graphics. So far I find two ways to make 3D text. halirutan in "Rotating an image along a Möbius strip?") ...
160 views

### DiscretizeGraphics issues with transformations

I noticed DiscretizeGraphics does not work correctly with transformed Graphics such as ...