Questions tagged [geometric-transform]

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92
votes
4answers
11k 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?
29
votes
2answers
1k 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: ...
19
votes
5answers
7k 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 ...
19
votes
1answer
3k views

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

I would like to distort or map a given JPEG so that it looks 3D when viewed from certain angle, as in this YouTube video. The most interesting part of the video: I usually use conformal mapping (a ...
16
votes
3answers
385 views

Weird behaviour when using Scale, Rotate in Graphics

Bug introduced in 8.0.4 or earlier and persisting through 11.2.0 or later (Edited to simplify drawing) I have a drawing of two tangent circles: ...
13
votes
3answers
1k 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
2answers
472 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 ...
13
votes
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://...
13
votes
2answers
814 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
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. ...
13
votes
2answers
207 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[] ...
12
votes
2answers
905 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: ...
12
votes
1answer
696 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 <...
11
votes
6answers
507 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
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 <...
9
votes
2answers
1k 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
137 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 ...
8
votes
1answer
345 views

Unexpected behavior of GeometricTransformation

Bug introduced in 8.0 or earlier and persisting through 11.2.0 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....
7
votes
2answers
1k 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
3answers
926 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
258 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. ...
7
votes
2answers
155 views

DiscretizeGraphics issues with transformations

I noticed DiscretizeGraphics does not work correctly with transformed Graphics such as ...
7
votes
1answer
336 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 ...
6
votes
3answers
204 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
3answers
326 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 ...
6
votes
1answer
387 views

Finding an optimal overlay of two point clouds

Imagine I have two sets of points: ...
6
votes
1answer
322 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 ...
6
votes
1answer
240 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: ...
5
votes
2answers
13k 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 ...
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 ...
5
votes
2answers
187 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 ...
5
votes
1answer
437 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 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 ...
4
votes
2answers
316 views

Rotating an Interpolating Function

I have used the following code to generate eigenfunctions of a PDE: ...
4
votes
3answers
510 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 ...
4
votes
2answers
224 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 ...
4
votes
1answer
292 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! ...
4
votes
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: ...
4
votes
1answer
769 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 ...
4
votes
1answer
103 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: ...
4
votes
1answer
208 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, it ...
4
votes
2answers
139 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?") ...
4
votes
1answer
90 views

Using RotationTransform and Table

I created a small animation, very simple of course, that works very well. ...
4
votes
0answers
96 views

Generation of Space Representation of non-crystallographic Point Groups

In Mathematica the command FiniteGroupData[{"CrystallographicPointGroup",<group number>}, "SpaceRepresentation"] yields the space representation (...
3
votes
1answer
292 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
80 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 ...
3
votes
1answer
297 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
2answers
473 views

Animation of a geometric transformation

This code: ...
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 ...