Questions tagged [geometric-transform]
The geometric-transform tag has no usage guidance.
89
questions
1
vote
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
votes
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
votes
2answers
79 views
1
vote
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
votes
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
votes
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 ...
0
votes
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
votes
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 ...
0
votes
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
vote
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
votes
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
votes
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 ...
0
votes
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
votes
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 ...
0
votes
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
votes
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
votes
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
votes
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
vote
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
votes
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
votes
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
vote
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 ...
1
vote
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
votes
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
votes
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
votes
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
votes
2answers
153 views
DiscretizeGraphics issues with transformations
I noticed DiscretizeGraphics does not work correctly with transformed Graphics such as
...
4
votes
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
votes
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
vote
1answer
156 views
Extracting scaling factor and rotation angle from TransformationFunction
I have successfully transformed two 2D data sets (data1, data2) by using ...
10
votes
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 <...
-4
votes
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
votes
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
vote
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
votes
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
votes
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
votes
1answer
88 views
Using RotationTransform and Table
I created a small animation, very simple of course, that works very well.
...
1
vote
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?
1
vote
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
votes
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
vote
2answers
167 views
13
votes
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
votes
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
votes
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
votes
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
votes
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
vote
1answer
175 views
2
votes
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
votes
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
votes
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 (...
