Questions tagged [geometric-transform]

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95 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 ...
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1answer
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 ...
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1answer
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 ...
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2answers
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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1answer
35 views

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 ...
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1answer
69 views

Visualizing an Affine Matrix

I have a computer graphics program that prints out affine matrices like ...
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1answer
58 views

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

Suppose I simulate a random walk in 3D using AnglePath3D[]: ...
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0answers
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: ...
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1answer
124 views

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

I have a shape given by ...
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0answers
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,...
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0answers
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 ...
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1answer
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 ...
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2answers
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: ...
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2answers
211 views

Why can't an annulus be mapped as a rectangle

The following code is used to map an annulus to a rectangle: ...
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2answers
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 ...
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0answers
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 ...
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0answers
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 ...
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1answer
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 ...
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2answers
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 ...
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1answer
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: ...
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1answer
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 $(x,y)\mapsto (\sqrt x,\sqrt y)$). ...
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1answer
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 ...
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1answer
79 views

Difficulty Displaying an Untransformed and Transformed Graphics3D Object with Show

Update: This bug has been fixed The bug has been fixed and the code below is working in $Version=12.1.1 for Microsoft Windows (64-bit) (June 19, 2020). Original ...
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2answers
122 views

LinearModelFit with Standardized data

I have a small data set of six points: ...
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1answer
121 views

Rotate a circle in 3D space with RotationTransform

This is related to my confusion over how to combine graphics objects and geometric objects: see Affine transformation of circular arc in 3D. Why does evaluating the ...
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3answers
387 views

Affine transformation of circular arc in 3D

Start with a quarter-circle of radius 1 centered at the origin and lying in the $xz$-plane: arc = ParametricPlot3D[{Cos[t], 0, Sin[t]}, {t, 0, π/2}] I want to ...
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2answers
302 views

Removing anomalous points from data

I have two sets of 2d-data points which can be transformed in each other by using a certain transformation function. The problem is that in both data sets there are points which do not have ...
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0answers
134 views

Transform a field with derivatives

Given a function of Cartesian coordinates $(x, y)$ in $g(x, y) = \frac{d}{dx}f(x, y)-y\frac{d}{dy}f(x, y)$, I want to transform this expression to polar coordinates $(r,\phi)$. I saw a solution using ...
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1answer
67 views

How is the error of FindGeometricTransform calculated? [duplicate]

This question has beeen asked here but was not answered. How is the returned error calculated? I cannot find any information about this in the documentation of ...
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1answer
97 views

Transforming a conic to it's standard form

Suppose a conic is given.I need to transform it to standard form.So i tried like this: ...
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1answer
69 views

Sequential 3D transformations

I have a function s[x,y,z] that assumes a reference of centered at the origin and pointed along the positive z axis. Given two points, I want to rotate and translate that function such that its center ...
2
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1answer
128 views

How to draw a “Y” shaped branch in Mathematica?

I want to draw a Y-shaped branch in Mathematica. I am trying to draw a line of length L. In step II, I want to translate to the ending point of the line. Then I want to rotate at an angle of 45 deg to ...
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3answers
955 views

Drawing the Pursuit curves

I was reading this post on Filling Space with Pursuit Polygons. I didn't really see where the filling was, but found it quite interesting. Then I saw these pursuit ...
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1answer
175 views

With equation of vector fields which are in cylindrical polar coordinates, how to plot 3-D vector field? [closed]

I have the equation of vector fields which are in cylindrical polar coordinates. How do I plot 3-D vector field? I never used Mathematica. Edit2: ...
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1answer
95 views

What algorithm is used by FindGeometricTransform? [closed]

Can anyone tell me how the operation FindGeometricTransform[pts1, pts2] works (I mean inside logic of the transformation function), or where can I find such an ...
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0answers
161 views

Eigenvalues not invariant after similarity transformation

I have two examples of matrices that undergo a similarity transformation: a random matrix, and an exclusion-process inspired matrix. The similarity transformation $\sigma$ is given by an $L \times L$ ...
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3answers
167 views

Computing angle of rotation and scaling factor directly from given transformation matrix

I have a simple 2D transformation matrix performing rotation combined with scaling \begin{bmatrix} 1 & 1 \\ -1 & 1 \end{bmatrix} Where the scalar $r$ is multiplied with \begin{...
4
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2answers
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 ...
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4answers
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 ...
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1answer
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 ...
5
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1answer
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 ...
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2answers
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[] ...
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2answers
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 ...
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0answers
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 ...
13
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2answers
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 ...
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1answer
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 ...
4
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2answers
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?") ...
7
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2answers
160 views

DiscretizeGraphics issues with transformations

I noticed DiscretizeGraphics does not work correctly with transformed Graphics such as ...
4
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1answer
304 views

Results of Rotate and Translate are not the same in 2D and 3D

I cannot understand why the same transformations in 2D and 3D do not give the similar results (flat join segment line). In 3D the segments are not joined. Please help! ...
2
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1answer
165 views

Transform a RegionFunction in ContourPlot3D

This is related to a previous question but now I would like to apply a geometric transformation to the region function first. (I am trying to paint a spot on a cylinder, where the spot is the region ...