# Tagged Questions

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149 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 ...
54 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 ...
121 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: ...
655 views

### Applying non-Affine transforms to 2D polygons with textures

I am trying to create a vanishing point perspective transformation of 2D polygons, for example transforming the red polygon into the blue polygon: ...
58 views

### How to get coordinates from GeometricTransform?

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

### Affine Transform Question

I set up these: ...
74 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....
45 views

### How to apply a shear matrix?

I have curves that I made to create a design using graphics[], and I wanted to apply a shear to this. I know/think that a shear comes in the {1,lambda}{0,1} form, and that I'm supposed to my multiply ...
770 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} } ...
66 views

### ImageForwardTransformation produces strange artifacts

I am trying to manipulate an image in equirectangular projection with ImageForwardTransformation. I want to change the projection's inclination to the ecliptic. For ...
51 views

### Generation of Space Representation of non-crystallographic Point Groups

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

### Rotating an Interpolating Function

I have used the following code to generate eigenfunctions of a PDE: ...
170 views

### Rotating a contour plot

I am working with some students on transforming conic sections by rotation of axes. I would like to create a simple Manipulate where I plot the before and after ...
89 views

### Eigenvectors choose intuitive ordering/sorting

Starting from some symmetric $L\times L$ matrices $M$(see below), I want to compute the eigenvectors in Mathematica, in order to construct an ...
972 views

### Movable text on a curve

Having an arbitrary curve defined as InterpolatingFunction, what is the best way to place a text on this curve? The text generally has two rows, for example: ...
262 views

### Unexpected behavior of GeometricTransformation

Bug introduced in 8.0 or earlier and persisting through 10.3 or later I have the following mapping on the complex plane: $$z \mapsto \tau \mu z-1,$$ where $\mu$ is complex, $\tau$ is real number....
315 views

### Coordinate system transformation problem (about Euler angle)

This question comes from the work that constructing the general cylinder by the NURBS. I have implemented the point-set $P_1,P_2,\cdots,P_n$ that in the $O-xyz$ plane, now I want to implement the ...
79 views

### Rotate the output of Plot3D [closed]

f[x_, y_] := Sin[x^2 + y^2] Exp[-x^2] + Cos[x^2 + y^2] g2 = Plot3D[f[x, y], {x, -2, 2}, {y, -2, 2}, PlotPoints -> 50, Axes -> False, Boxed -> False] ...
159 views

### Applying transformations to data coming from an STL file

I am very new with the use of 3D graphics in Mathematica, so my question might be very naive. I need to Import an STL file, apply transformations to it (rotation and translation), and export it back ...
299 views

### Weird behaviour when using Scale, Rotate in Graphics

Bug introduced in v8.0.4 or earlier and persisting through 10.3.0 (Edited to simplify drawing) I have a drawing of two tangent circles: ...
130 views

### Log transformation (in dimensions) of an image

Is there an easy way to do a log-transformation of an image? I'm not taking about the colours, but the geometry. The difficulty is to extrapolate pixels and round-offs. For example, an white image ...
376 views

### Volumetric Rendering of cylinder symmetric radial image

I would like to render a cylinder symmetric radial cross-section with Image3D. As an example one could use the propagation of a Bessel Beam through a Lens: Here the cylinder axis is the bottom of ...
170 views

### Easy way to bind rect to geometrical 2D line?

I got stuck with the following problem. For some calculation and visualization purposes I need to draw different shapes (like rectangle) with proper slope on custom line. The trivial example: ...
170 views

### What kind of algorithm can be used to map image coordinates to cylinder coordinates

I plan to flatten an images on curved surface(eg: jar or door knob) and I found a pretty good post which helps me a lot :)(link below). However, I still confuse on how to map image coordinate to ...
203 views

This code: ...
64 views

### Using TransformationFunction

I try to use the result from the function FindGeometricTransform. It returns an error and a TransformationFunction. The TransformationFunction is technically a 4x4 matrix. But how can I use the ...
396 views

### Make a series of points curl

Say I have a series of points that make a straight line... (Fig 1) points = {{0, 0, 0}, {1, 0, 0}, {2, 0, 0}, {3, 0, 0}, {4, 0, 0}, {5, 0, 0}} I can rotate these ...
2k views

### How to map an image to get an illusion of 3D

I would like to distort or map a given jpg so it looks 3D when viewed from certain angle, as in the following youtube video: http://www.youtube.com/watch?v=IfCCUd8mFtg. The most interesting part of ...
224 views

### Translate Image respect to its centroid

To apply DistanceTransform for shape recognition, I want to center all images in a fixed point {cx,cy}. I mean each image's centroid should be ...
277 views

### Finding an optimal overlay of two point clouds

Imagine I have two sets of points: ...
399 views

### Compose many Geometric Transformations for 3D Graphics

I'm struggling to understand what would be a good way to compose several geometrical transformations to create a single TransformationFunction to be applied to a <...
5k views

### How to draw a great circle on a sphere?

I apologize for the text description, but new users are not allowed to post images. I want to draw a circle that cuts through the center of a sphere and has an inclination of 15 degrees with the ...
143 views

### Region plot of transformed region giving odd result

I tried applying a transformation to a rectangle: RegionPlot[TransformedRegion[Rectangle[{0, 0}, {1, 1}], {#1^(1/3) + #2, 1 + #2} &]] giving In reality, ...
245 views

### Plotting in projective space

I am having difficulty figuring out how to plot to projective space. Suppose I have a region which I have plotted such as: ...
824 views

### How to get UV mapping of 3D tube

Here is cylinder data: file We can mesh the surface, thanks to lalmei, Belisarius and Simon (link) How to achieve uv mapping from a 3d straight and curved tube? Working code: ...
106 views

### Geometric Transformation not working - degenerate points?

I've successfully used FindGeometricTransformation to project the simplex triangle onto the x-y plane: ...
258 views

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258 views

### Find the centre of FindGeometricTransform

I'm interested in using Solve[] to find the centre point of rotation (as an $x,y,z$ coordinate point) and axis of rotation (as a vector) from a ...
758 views

### Is it possible to manipulate a graphics object with 3 rotation transforms simultaneously?

The code that I have written has an unintended consequence that I'm not sure how to get around. I want 3 rotation transforms to be applied simultaneously to 1 graphics object. Instead, I get 3 ...
640 views

### Identifying when two graphic objects overlap

I'm designing a small demonstration that helps to visualize the reason behind shaping an electrode that is used to probe a surface: ...
379 views

### Custom TransformationFunction in Graphics? GeometricTransformation::nonaffine error

There are many functions in Mathematica, which return expressions with TransformationFunction head, for example RotationTransform. Unfortunately, there is no ...
305 views

### point-wise transform of Plot

Suppose I have the following plot: Plot[(1 - p2)^2/(p2^2 + (1 - p2)^2), {p2, 0, 1}, AxesLabel -> {"p2", "p1"}] Now I want to do a point-wise transform to ...
438 views

### Using ImageTransformation[] with a lookup table

I need to transform images by ImageTransformation in a time critical application. Therefore I precalculate a lookup table lut of ...
162 views

### Reflection transform of function [duplicate]

I am trying to find the reflection function. Here is my function and its graph. ...
911 views

### Rotate a grid, made up of lines, so that it aligns with the xy axes

While working on an answer for another problem I hit upon one of my own. I took the image given in that question and cleaned it up so that I could detect the grid lines: ...
321 views

### Digital Elevation Maps (DEM) are Warped yet ReliefPlot renders as a rectangle - how do i join?

I downloaded several USGS Digital Elevation Maps (DEM files) corresponding to 12 adjacent areas. Each file Imports[] into Mathematica and I can render the individual ...
274 views

### How to transform and swap columns of this matrix in a simple way? Version 2

So, earlier today I asked the question How to transform this matrix & swap its columns in a simple way? and was given useful and elaborated answers. Now, I'm still not used to the "Array", "...
524 views

### How to transform this matrix & swap its columns in a simple way?

I would like to transform matrix $\mathbf A = \begin{pmatrix} a&b&i&j\\ c&d&k&l \\ e&f&m&n \\ g&h&o&p \end{pmatrix}$ into matrix \$\mathbf B = \begin{...