Questions tagged [geometric-transform]

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1answer
38 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 ...
0
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1answer
40 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 ...
2
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2answers
79 views

LinearModelFit with Standardized data

I have a small data set of six points: ...
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1answer
65 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 ...
6
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3answers
314 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 ...
5
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2answers
180 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
69 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 ...
2
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1answer
54 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
81 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: ...
1
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1answer
61 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
82 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 ...
4
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3answers
468 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
69 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: ...
3
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1answer
79 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
115 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 $L \times L$ ...
2
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3answers
122 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
219 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 ...
5
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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 ...
1
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1answer
220 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 ...
6
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1answer
290 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 ...
13
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2answers
202 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[] ...
1
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2answers
247 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
47 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
460 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 ...
0
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1answer
127 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
137 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
153 views

DiscretizeGraphics issues with transformations

I noticed DiscretizeGraphics does not work correctly with transformed Graphics such as ...
4
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1answer
291 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
126 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 ...
1
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1answer
156 views

Extracting scaling factor and rotation angle from TransformationFunction

I have successfully transformed two 2D data sets (data1, data2) by using ...
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1answer
110 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 <...
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1answer
139 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?
2
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1answer
131 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 ...
1
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0answers
256 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 ...
5
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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 ...
6
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1answer
234 views

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

Bug introduced in 8 or earlier and persisting through 11.2.0 Consider the following code: ...
4
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1answer
88 views

Using RotationTransform and Table

I created a small animation, very simple of course, that works very well. ...
1
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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?
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2answers
183 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 ...
13
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1answer
609 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. ...
1
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2answers
167 views

Translate graphics from a contour plot to tile a plane

MWE: ...
13
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2answers
2k 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://...
3
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1answer
287 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 ...
3
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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 ...
4
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1answer
194 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: ...
2
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1answer
97 views

How to get coordinates from GeometricTransform?

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

Affine Transform Question

I set up these: ...
2
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1answer
336 views

Plotting a manifold within an existing surface

I have a dynamical system $\textbf{x}'=\textbf{f(x)}$ where $x\in \mathbb{R}^4$. However, $x_1 +x_2 +x_3 + x_4 =1$ and $0\leq x_i \leq 1$ for $i = 1,2,3,4$, meaning the system lives on the Tetrahedron....
5
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2answers
12k views

How do I get the inverse of a homogeneous transformation matrix?

I want to get the inverse of this homogeneous transformation matrix: iab = { {1, 0, 0, 0}, {0, 0, -1, 0}, {0, 1, 0, 3}, {0, 0, 0, 1} } using the ...
4
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0answers
94 views

Generation of Space Representation of non-crystallographic Point Groups

In Mathematica the command FiniteGroupData[{"CrystallographicPointGroup",<group number>}, "SpaceRepresentation"] yields the space representation (...