Questions tagged [transformations]
Transformations are mathematical operations that can be applied to an object to change its scale, position and orientation.
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What kind of transformation when the aspect is changed for a rotated shape?
I have a geometric shape (assuming that is a rectangle). I want to rotate it about it geometric center by an angle of 45° and plot the result using matplotlib with an equal aspect ratio, I get ...
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43 views
Estimate 3D cube pose after camera rotation
I have some photos of 3D cube. I also know the 3D pose of the cube in each photo (yaw, pitch, roll).
I want to estimate the new pose (yaw, pitch, roll) of the cube after performing 2D rotation to the ...
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30 views
Transformation for aligning 3D object with reference frame of 3D turtle graphics
The problem
I'm using a 3D extension of the well-known "Turtle graphics" to draw plants. My system works by maintaining a position $\vec{p}$ and three vectors:
The heading $\vec{H}$
The "up" ...
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33 views
Apply transformation to single vertices in OpenGL in order to deform mesh
I'm making a 2D cell simulation game.
The mesh for my cell is basically just a manually-generated triangle fan that looks like this.
I would like to reproduce the wobbling/vibration effect on the ...
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2answers
59 views
Visualize the interpolated unit quaternion on the surface of the unit sphere
My major is mechanical, please forgive me for asking questions that may seem trivial to you.
First, I'm reading the following paper:
Dam, Erik B., Martin Koch, and Martin Lillholm. Quaternions, ...
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1answer
69 views
Compute Speed of Spheres in 3D animation
I have created two animations:
One where a "camera" moves towards the spheres creating an optic flow (1st GIF).The code can be found here.
One where spheres move randomly in a 3D coordinates space (...
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0answers
23 views
What quad will fill the screen, which can be inverse-projection-view transformed to map to the near frustum plane?
I've been experimenting with raytracing using GLSL. I had success rendering a cube which encloses the object.
Now I want to do a full-screen raytrace, and I want to construct a quad which covers the ...
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1answer
49 views
Can pixels on the image plane be mapped to world space coordinates?
I'm trying to learn the fundamentals of 3d computer graphics by writing a toy framework in WebGL.
I'm currently working on mouse based camera controls. There are plenty of good resources in the ACM ...
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81 views
Help with understanding the look-at function (the view matrix)
I've been reading this article about the look-at function. I don't understand the part when they're trying to inverse the matrix N.
They say that R is orthogonal because all its row and column ...
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1answer
73 views
Use glTranslatef and shaders?
In newer OpenGL it's encouraged to use shaders and pass the model-view-projection as parameters. But what if I drew a complex object, and wanted to translate/rotate it and draw many copies?
For ...
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2answers
338 views
How can i create a 3D Sphere(earth) using OpenGL, GLFW, GLAD, GLM?
Please help me out with this thing and currently i am a little more than a beginner so please tell me in that context. i don't need any obsolete methods for creating this like using GLUT or GLEW.can ...
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23 views
Customized editing of a 2D bitmap
Please excuse this basic question, as I'm new to computer graphics.
Let's say I have a sprite that looks like below.
I wish to programmatically transform the sprite such that the bitmap looks like ...
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47 views
Moving a sphere in a basic ray tracer
I have written a really basic ray tracer. It generates primary rays and sets the colour of the pixel to the colour of the object that I have set myself. The code for which can be seen below.
...
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0answers
27 views
How to find matrix that projects 3d points into 2d plane centered in the origin?
I have a list of 3D points defined by Cartesian coordinates, i.e. [(x1,y1,z1), (x2,y2,z2), ..., (xn,yn,zn)]. I want to project them to a 2D plane which has origin in the center (0,0,0) but which is ...
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1answer
74 views
What are affine covariant regions
I am trying to understand this seminal paper. I read this post on what affine transformations and my understanding is that affine transformations are transformations that preserve parallelism of lines ...
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1answer
66 views
Inflate 3D mesh into sphere
I am after a simple (not necessarily efficient) algorithm to "continuously" transform a closed surface mesh into a sphere.
It seems that Blender is able to do this quite well: https://docs.blender....
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1answer
599 views
What is the difference between world coordinate, viewing coordinate and device coordinate in computer graphics?
The 2D pipeline involves with the construction of world coordinate scene followed by converting world coordinate to viewing coordinate, then transforming viewing coordinate to normalized coordinate ...
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2answers
109 views
How to calculate interpolation between multiple skeleton poses?
I found out that I should use spherical linear interpolation to blend two poses of a joint. I cannot find what to do if I have hundreds of poses to blend except applying the SLERP iteratively.
What ...
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1answer
138 views
Camera Model View transformation in Ray Tracing
I am implementing my own simple ray tracing and I came across some sort of confusion. When defining the verticies in the world I multiply them by the modelView transformation system (the matrix ...
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1answer
36 views
How to scale primitive shapes [in Blender] so that they are within a [unit] sphere?
I wonder how is it possible to scale all shapes so that they are within boundaries of a [unit] sphere? I know how to do this for a cube: if radius of the sphere is S...
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1answer
101 views
Ray tracing the next week: understanding Instances
My question is not about the code, but it's about the approach used by the author Peter Shirley (and apparently common practice in ray tracers) of handling Instances. To understand the question it's ...
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2answers
147 views
transformation from cartesian coordinates to spherical coordinates without calculations
Given this graph in the 3d cartesian coordinates i should figure out the spherical coordinates representation but without the use of calculations .
I've been trying to solve this the whole day but i ...
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2answers
69 views
Using transformations to get from A to B image
I try to solve this,
First, I used scaling: $Scale(S_x,S_y)=S(\sqrt 5,\sqrt 5)$
So, I enlarge the bottom of the house and the sides, to the same size of B image.
Later, I used rotation: $R(\theta)=...
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1answer
47 views
Define position and orientation in a local coordinate system
Suppose we have a world coordinate system W and a 3D model m1 defined in W. ...
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2answers
338 views
How to convert from Object space into World space (exercise from 3D Math Primer book)
This is not homework. I'm self studying Computer Graphics, using the book "3D Math Primer for Graphics and Game Development" (2nd edition). So there is the exercise 6 in chapter 3 which I can't figure ...
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1answer
60 views
My 2D translation matrix causes the box to be off screen when it shouldnt be
Now I know this isn't the way this is normally done so please bear with me. I am doing this this way so I know I have a solid conceptual understanding of everything that goes beyond example code.
I ...
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0answers
32 views
Transforming arcs and perspective change
I have a SVG with group of independent arcs that move around common origin.
On user event those arcs can change both their radii and start/end angles.
On other user event the user can change view from ...
2
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1answer
313 views
Bump mapping with triangles and height maps
I'm trying to add bump mapping to my ray tracer, and I'm currently struggling to add bump mapping to it, as I don't seem to get the transformations from texture space to world space correctly.
I have ...
3
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1answer
206 views
Need help with change of basis (world to camera frame)
I'm reading up on coordinate systems and geometric transformations but the change of basis topic still confuses me. I found this exercise but, honestly, I wouldn't know how to begin:
Given a world ...
2
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1answer
76 views
Composition of decomposed transformations
Say I have a scene graph, and each node has a scale, rotation, and translation. Can I combine these into a single scale, rotation, and translation?
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2answers
257 views
Rotate a model or a view with mouse input to produce intuitive results
I am writing 3D graphics software in Java using the LibGDX framework (which is a front-end for OpenGL), and am baffled by a transformation problem. How do I rotate the orientation of the camera or ...
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1answer
120 views
preserving z-values during projection?
Consider this figure for projection.
There are two equations that give value for the xp and yp coordinates:
$x_p=x.\frac{(z_{vp}-z_{prp})}{h}+ x_{prp}.\frac{(z-z_{vp})}{h}$ and
$y_p=y.\frac{(z_{vp}...
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1answer
118 views
What is the equivalent of rotation matrix in Euler angle space for Quaternions?
I have to load a mesh in Blender (which uses Z and Y as up and forward axes), modify it and export it (with setting up and ...
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1answer
62 views
How to rotate a shape in another 3D software so that the rotation matches with the rotation in Blender?
I import a mesh in Blender, export it with setting axis_forward='-Z', axis_up='Y', import in NVIDIA's FleX, rotate it and store it on disk; I call this mesh ...
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1answer
82 views
How to compute A and B in projection matrix
I'm trying to compute a projection matrix to transform from view space to NDC with a near clip plane at -1 and far plane at +1. The general form of this matrix (disregarding aspect ratio and focal ...
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1answer
98 views
How do I derive this transformation
If I had two right handed frames where one has vectors [i, j, k] and another with corresponding vectors [u v w], how would I derive the transform M[i j k] <-- [u v w] when applied to any point P in ...
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0answers
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How can I register an articulated model to noisy predictions?
Given point sets $Y$ and $M$, I'd like to register articulated $M$ to $Y$ without changing the edge distances of $M$. The point correspondences between $Y$ and $M$ are known and points have a fixed ...
2
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1answer
145 views
Deciphering Affine/Projective Transformation Code
I've spent about 2 days trying to understand this piece of code (from here) that applies an affine/projective transformation to an image. I will link bits of the code that I'm struggling to understand ...
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0answers
45 views
What is wrong with my deformation gradient calculation?
I created two ellipses,$\hspace{150px}$,where the red ellipsis is as the blue one, except translated to the right and rotated by ${30}^{\circ} .$ Using rotation matrix,
$$
\left[
\begin{array}{cc}
...
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3answers
237 views
Rotation of a random unit vector at a point in 3D space by an angle
I have a scenario where I need rotate a vector ( unit vector) at a point in space by an angle along Z-axis. Is it possible to help me to understand a procedure to achieve this. I'm using vb.net ...
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0answers
165 views
How to apply scale, translate, rotate with different origin and get new rectangle coordinates
I was reading other questions in this topic but I couldn't apply any viable solution to solve my use case.
I have a crop area described with two dimensions (cropWidth, cropHeight)
I can easly compute ...
2
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1answer
41 views
Correctness or otherwise of the procedure for generating an orbiting camera in WebGl
I have to create a orbiting camera. I created the model of sun (a sphere) around (0,0,0) , triangulated and Phong shaded it. I would have a camera that goes around the sun thus an orbiting camera and ...
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0answers
2k views
General fixed-point scaling
For general fixed-point scaling problem, If I want to scale twice about a fixed point (x, y), I need to first translate the object so that fixed point coincides with the origin, then do the scaling ...
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1answer
112 views
Rotating scene or complex object using center of AABB
All objects have two AABB (Axis Aligned Bounding Box), one in local space and one another in world space. The box in local space is calculated while importing scene from external source, and the box ...
3
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0answers
88 views
Linear bending of a mesh
I am trying to implement linear bending of a mesh by following what Alan H. Barr explained in his Global and local deformations of solid primitives paper (ACM link, Direct Link hosted on a faculty ...
4
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1answer
245 views
Canonical Space to Screen Space: Why do we have the strange -0.5?
When we convert from canonical space to screen space,
To map x from -1 to 1 to 0 to width,
...
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1answer
377 views
Curve rotation in GLSL fragment shader
I'm trying to figure out the correct math to rotate and translate a curve displayed in a fragment shader.
What I try to accomplish is to define a curve, for example a sine curve, in a local ...
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1answer
913 views
How do I build my tangent space matrix?
I'd like to understand how the process of building the "tangent space" matrix for normal mapping works. I'm following several tutorials, and other stackexchange questions, but I'm unfamiliar with the ...
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0answers
48 views
Transform a cube in a truncated pyramid
I have to calculate the modeling transformation that transforms a cube of side=1 centered in (0,0,0) in a rectangular truncated pyramid of height=2,sides of basic rectangle equals to 3 and 2, sides of ...
3
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1answer
1k views
Ray tracing: transforming ray to object's local space for intersection test
Im writting a raytracer, for which I want to be able to test intersections with implicit surfaces (in my case spheres). Without applying any transformation it works great, but I would like to upgrade ...
