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81
votes
4answers
8k views

How to peel the labels from marmalade jars using Mathematica?

How can I detect and peel the label from the jar below (POV, cylinder radius, jar contents are all unknown) to get something like this, which is the original label before it was stuck on the jar?
25
votes
2answers
958 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: ...
17
votes
5answers
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 ...
15
votes
3answers
306 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 ...
13
votes
3answers
902 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: ...
13
votes
1answer
1k 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 ...
13
votes
2answers
296 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: ...
11
votes
2answers
648 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: ...
10
votes
5answers
394 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 ...
10
votes
1answer
394 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 <...
9
votes
2answers
818 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: ...
8
votes
1answer
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 ...
7
votes
3answers
631 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: ...
7
votes
2answers
742 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 ...
7
votes
1answer
260 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....
6
votes
3answers
168 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: ...
6
votes
1answer
320 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 ...
5
votes
1answer
271 views

Finding an optimal overlay of two point clouds

Imagine I have two sets of points: ...
5
votes
1answer
126 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 ...
5
votes
1answer
375 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 ...
4
votes
2answers
256 views

Rotating an Interpolating Function

I have used the following code to generate eigenfunctions of a PDE: ...
4
votes
1answer
112 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: ...
4
votes
1answer
159 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 ...
3
votes
2answers
663 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} } ...
3
votes
4answers
512 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{...
3
votes
3answers
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", "...
3
votes
1answer
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 ...
3
votes
1answer
142 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, ...
3
votes
0answers
43 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 ...
3
votes
0answers
49 views

Generation of Space Representation of non-crystallographic Point Groups

In Mathematica the command FiniteGroupData[{"CrystallographicPointGroup",<group number>}, "SpaceRepresentation"] yields the space representation (...
2
votes
3answers
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 ...
2
votes
1answer
71 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....
2
votes
1answer
241 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: ...
2
votes
2answers
155 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 ...
2
votes
2answers
201 views
2
votes
1answer
88 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 ...
1
vote
3answers
304 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 ...
1
vote
2answers
63 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 ...
1
vote
1answer
376 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 ...
1
vote
1answer
87 views

Affine Transform Question

I set up these: ...
1
vote
1answer
51 views

How to get coordinates from GeometricTransform?

I'm trying to get the exact coordinates of the resulting points from my transform: ...
1
vote
2answers
257 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 ...
1
vote
1answer
136 views

Why doesn't Normal[] work?

I have a polygon on which I'm applying a GeometricTransform and I want to get the coordinates of the transformed polygon. ...
0
votes
1answer
167 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 ...
0
votes
1answer
74 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] ...
0
votes
0answers
44 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 ...
0
votes
0answers
106 views

Geometric Transformation not working - degenerate points?

I've successfully used FindGeometricTransformation to project the simplex triangle onto the x-y plane: ...
0
votes
1answer
161 views

Reflection transform of function [duplicate]

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