Questions tagged [geometric-transform]

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Strange behaviour in GeometricTransformation

I came across the following strange behaviour with the GeometricTransformation function. ...
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1 answer
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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.
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2 answers
143 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 ...
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3 votes
2 answers
93 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 ...
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2 votes
0 answers
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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: <...
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1 vote
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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 <...
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1 vote
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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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3 votes
1 answer
75 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 ...
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1 answer
75 views

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 ...
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-1 votes
1 answer
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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 ...
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1 vote
1 answer
141 views

How to use VectorAngle[] in AnglePath3D[]?

Suppose I have a specific angle that I calculate from two vectors, in 3D: ...
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2 answers
105 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 ...
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1 vote
2 answers
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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: ...
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1 answer
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On the geometric transformations of polygons

Each starry set has the following property: ...
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0 answers
72 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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5 votes
2 answers
178 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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2 votes
0 answers
45 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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99 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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1 vote
2 answers
167 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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11 votes
2 answers
423 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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2 answers
200 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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4 votes
0 answers
156 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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5 votes
1 answer
112 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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2 votes
2 answers
101 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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1 answer
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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 ...
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1 vote
1 answer
114 views

Visualizing an Affine Matrix

I have a computer graphics program that prints out affine matrices like ...
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1 vote
1 answer
96 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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0 votes
0 answers
30 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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3 votes
1 answer
184 views

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

I have a shape given by ...
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4 votes
0 answers
206 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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0 votes
1 answer
87 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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  • 303
3 votes
2 answers
115 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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  • 479
4 votes
2 answers
240 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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8 votes
2 answers
689 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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  • 1,303
0 votes
0 answers
70 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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2 votes
1 answer
103 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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1 vote
2 answers
351 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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6 votes
1 answer
199 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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  • 625
1 vote
1 answer
98 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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  • 311
1 vote
1 answer
87 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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2 votes
1 answer
99 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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2 votes
2 answers
168 views

LinearModelFit with Standardized data

I have a small data set of six points: ...
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1 vote
1 answer
192 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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  • 11.3k
6 votes
3 answers
448 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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5 votes
2 answers
446 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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  • 11.3k
0 votes
0 answers
183 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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2 votes
1 answer
83 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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0 votes
1 answer
155 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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1 vote
1 answer
83 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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  • 2,209
2 votes
1 answer
140 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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