Questions tagged [geometric-transform]

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1answer
55 views

On the geometric transformations of polygons

Each starry set has the following property: ...
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21 views

Convert function to convex on infinite range, knowing gradient and hessian

Let's take a function $f=sech(x)$ as an example. It is strongly convex in a limited range of $x$. It is further assumed that: $f$ is a "black box", $x$ as input ; output is the value of the ...
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Normal of Translate works in 3d but not 2d [duplicate]

Edit: in light of these links, I suppose I'm beating a dead horse here. Normal is inconsistent, that's not technically a bug, just slightly disappointing Why doesn&...
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43 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 ...
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2answers
147 views

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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34 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 ...
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70 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 ...
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1answer
101 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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2answers
394 views

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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2answers
153 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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124 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
111 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
79 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
41 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
83 views

Visualizing an Affine Matrix

I have a computer graphics program that prints out affine matrices like ...
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1answer
71 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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29 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
151 views

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

I have a shape given by ...
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0answers
198 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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1answer
81 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
104 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
232 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
656 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
54 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
91 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
283 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
173 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
82 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
78 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
92 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
145 views

LinearModelFit with Standardized data

I have a small data set of six points: ...
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1answer
156 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
417 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
395 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
155 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
75 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
125 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
75 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 ...
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1answer
133 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
1k 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
229 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
104 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
169 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
269 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{...
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2answers
257 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
965 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
453 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
506 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
250 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
385 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 ...