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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 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
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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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86 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
25 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
81 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
76 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
66 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
35 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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133 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
54 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
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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 ...
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1answer
159 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 ...
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1answer
115 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 ...
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1answer
50 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
143 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
74 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
50 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
58 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
62 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
97 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 ...
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1answer
104 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
44 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
174 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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56 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 ...
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1answer
39 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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1k 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
87 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 ...
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86 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 ...
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1answer
212 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
252 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
435 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
40 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 ...
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1answer
763 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 ...
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1answer
132 views

What is the algorithm used in pbrt-v3 for triangle intersection?

Where's this algorithm come from? Any references? And a specific question, when the authors compute the transformation from world space to ray-triangle intersection coordinate space, what's the ...
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0answers
47 views

Tanget plane of an image

My problem is about tangent plane. I have an image (m by n). I obtain surface normal vector using machine learning methods. Then i would like to obtain tangent plane for this surface normal. To ...
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1answer
103 views

Back and forth rotation on Y-axis

I want to write code for a cube rotating 10 degrees back and forth on its y-axis in an OpenGL application. Right now I have this written in my display method, however it depends on processor speed, ...
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1answer
59 views

Do normals in obj files have to be changed into eye coordinate before being used?

Obj files give pre-calculated normals which are in model coordinates. So I wonder if they have to be transformed into eye coordinate (where I use them to calculate lighting)? I'm thinking yes because ...
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1answer
634 views

Why does this gl_FragDepth calculation work?

I am raytracing in GLSL. My gl_FragDepth calculation wasn't right, so I did some hunting and found this solution (P is the world-...
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2answers
110 views

Is there something wrong with a column camera matrix?

I am writing a simple ray tracer. I was working on my camera matrix when I encountered a problem. When I changed the look vector, so that it headed down, the image, which was supposed to go up, ...
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1answer
110 views

What technique would I use to create fake 3d walls as seen in Realm of the Mad God

I wanted to make a little demo for a console with Realm of the Mad God esc graphics to brush up my C and SDL skills. One problem I'm running in to is creating the 3D walls. The console I'm ...
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1answer
66 views

Image warping using pixel normals

I want to insert a logo into an RGB image with proper 3D transformations. I can get the estimated pixel normals of this image using the code here: https://github.com/yindaz/surface_normal. Pixel ...
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0answers
187 views

Octahedral mapping for Spherical functions

I guess most of you are familiar with environment maps, they represent distant lighting distribution, and are used to render objects given their BRDF or SVBRDF distribution. Many papers map the ...
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1answer
300 views

why is translating in 3D space the same as shearing in 4D space?

I was reading "3D Math Primer for Computer Graphics and Game Development" and there was something the author had said that I thought was particularly interesting, he stated It is important to ...
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1answer
142 views

How to obtain generalized barycentric coordinates for n-sided polygon?

Quadrilateral linear basis functions(generalized barycentric coordinates) are defined as: What are the steps to calculate the above functions? Is it possible to obtain basis functions for a 5 sided ...
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120 views

Composition of an .obj file

Using an iPhone X, I can get a mesh of the face (using ARFaceGeometry), which I can output as an .obj file using ...
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1answer
133 views

How to calculate camera distance so that after projective transformation a quad is filling the whole screen

First of all, I'm using OpenGL and GLM. Now, I have a square perpendicular to the z-axis and centered around it. Let's say that it has Z-value (offset along the Z-axis) X. Now, I want to set up a ...
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2answers
396 views

OpenGL : How to rotate an object around viewing space x-axis

I have an object(cow). This cow was translated and rotated(with arbitrary axis) in the modeling space for several times. And I can't know how much cow is translated or rotated. Only I can obtain is ...
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2answers
41 views

How to get the length of paths in an given font/character

I wan't create some LED-rope text, using some script font, like the following: For this I need somewhat estimate the needed length of the LED-rope for the given letter (or combinations of letters). ...
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2answers
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Supporting multiple camera types in a deferred renderer without specializing the shaders or in the shaders

Perspective Camera A (row-major) perspective transformation matrix has the following format: $$\begin{align} \mathrm{T} &= \begin{bmatrix} \mathrm{T}_{00} &0 &0 &0 \\ 0 &\...