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# Questions tagged [geometric-transform]

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### 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 ...
1answer
126 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: ...
1answer
48 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 $(x,y)\mapsto (\sqrt x,\sqrt y)$). ...
1answer
50 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 ...
1answer
45 views

### Difficulty Displaying an Untransformed and Transformed Graphics3D Object with Show

I would like to illustrate a sequence of translations and rotations relative to the initial coordinate system simultaneously with multiple views using Manipulate. I discovered that there are some ...
2answers
85 views

### LinearModelFit with Standardized data

I have a small data set of six points: ...
1answer
78 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 ...
3answers
333 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 ...
2answers
195 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 ...
0answers
79 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 ...
1answer
55 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 ...
1answer
83 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: ...
1answer
62 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 ...
1answer
84 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 ...
3answers
543 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 ...
1answer
94 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: ...
1answer
83 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 ...
0answers
128 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 $L \times L$ ...
3answers
124 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{...
2answers
226 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 ...
4answers
956 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 ...
1answer
261 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 ...
1answer
332 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 ...
2answers
209 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[] ...
2answers
273 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 ...
0answers
51 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 ...
2answers
473 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 ...
1answer
131 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 ...
2answers
140 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?") ...
2answers
155 views

### DiscretizeGraphics issues with transformations

I noticed DiscretizeGraphics does not work correctly with transformed Graphics such as ...
1answer
295 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! ...
1answer
132 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 ...
1answer
163 views

### Extracting scaling factor and rotation angle from TransformationFunction

I have successfully transformed two 2D data sets (data1, data2) by using ...
1answer
113 views

### What does the alignment error returned from FindGeometricTransform measure?

FindGeometricTransform returns "the alignment error together with the transformation function." How is the alignment error computed? I ask because if you iterate <...
1answer
146 views

### Mathematica Module for Denavit-Hartenberg Parameters to Transformation Matrix

I need to write a Mathematica module to get a 4*4 transformation matrix given the Denavit-Hartenberg parameters of the manipulator. How do I go about it?
1answer
148 views

### Get CoordinateTransformData from TransformationFunction?

I can define a composite symbolic transformation as e.g. tf = RotationTransform[θ, {0, 0, 1}] @* TranslationTransform[{0, 0, 1}] which returns (in ...
0answers
291 views

### Apply a four-point transform crop to an image

I am attempting to straighten and crop an image by using Edge Detection. The original image looks like this. By using edge detection and finding the max and min values for the points regarding the ...
0answers
197 views

### BSpline: construct surface from enclosing contours

I'm aiming to construct 3D shape from profiles (typical archaeological drawing stuff: front, side and top profiles views). Through several operation, I now have BSpline curves, which should define ...
1answer
241 views

### Plot points shifted (a lot) in output and PNG export but not in PDF export

Bug introduced in 8 or earlier and fixed in 12.0.0 Consider the following code: ...
1answer
91 views

### Using RotationTransform and Table

I created a small animation, very simple of course, that works very well. ...
1answer
77 views

### Implementation of ShearingMatrix

How does Mathematica implement ShearingMatrix? In other words given the parameters $\theta$, $n$ and $v$, what is the formula behind it?
2answers
213 views

### Images and Linear Transformations

I was playing around with some of the Image processing commands like ImageRotate. I thought it would be fun to try and make up some basic linear transformation rules - starting in 2D and then going ...
1answer
612 views

### How to align a poster?

I'd like to crop and transform out the magazine cover so that it is rectangular. I read the docs for ImagePerspectiveTransformation, and here's where I got to. ...
2answers
177 views

MWE: ...
2answers
3k views

### Application of the projection matrix: Removing perspective distortion

I know that there are many posts about image treatment, but I still have trouble with this little challegene. Baisically I want to remove the perspective distorsion form this image: (source: http://...
1answer
299 views

### Projecting a Graphics3D object onto a plane

I would like to project a 3-dimensional cone onto a plane and mark the intersection (which is an ellipse) with a line. I find cone2 by performing a transformation ...
0answers
103 views

### TransformedRegion and RegionPlot

I encountered an issue using RegionPlot together with rotated regions. Notice how as long as one drags a slider in this simple ...
1answer
196 views

### Getting Area of a region transformed by GeometricTransformation

I tried this: Clear[b1, b2, A, p] b1 = {-1, 1}; b2 = {1, 1}; A = {{2, 1}, {-1, 1}}; p = Parallelogram[{0, 0}, {b1, b2}]; Then drew this: ...
1answer
100 views

### How to get coordinates from GeometricTransform?

I'm trying to get the exact coordinates of the resulting points from my transform: ...
1answer
179 views

### Affine Transform Question

I set up these: ...