Questions tagged [matrix]

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How to unproject quadrilateral into rectangle?

tl;dr: Math problem in projective geometry: How does one find some 4x4 camera matrix that gives a projection as illustrated below, such that points A,B,C,D are somewhere on the edges of the unit box (...
1k views

Why are width and height divided by 2 in the perspective projection matrix?

I'm using OpenGL to learn computer graphics. I'm trying to understand projection matrices. The following are shown in the OpenGL 'Red Book': I don't understand why the width and height are divided ...
587 views

Animating a smooth linear transformation

After watching this video on matrices, I tried to make a simple animation of 2D linear transformations. Starting with a set of 2D points in a grid, I applied a 2x2 matrix to each point and obtained a ...
4k views

How to translate object to origin?

I want to rotate a 3D object. On this website http://paulbourke.net/geometry/rotate/ the first step says: (1) translate space so that the rotation axis passes through the origin What is meant by "...
78 views

Confusion about notation in a paper

I have been trying to understand "Fast Simulation of Mass-Spring Systems" by Liu et al., which can be found here. There is one part in the methods section that is confusing me. Just after equation 12, ...
457 views

Do we use 3x3 matrices in computer graphics?

I've been doing some side-research on computer graphics as a hobby and came across this article on quaternions: http://www.opengl-tutorial.org/assets/faq_quaternions/index.html#Q2 In the first ...
726 views

How is that possible that matrices can be thought as coordinate systems?

I've been reading around that matrices (for example, rotation matrices, but not only) can be thought somehow as coordinate systems. My question is: how is that possible? I've seen for example that ...
217 views

Graphics Pipeline: Viewspace & Back face culling incorrectly

I'm attempting to model a simple graphics pipeline - using Matlab at the moment as a modelling tool to get the transformations correct. I appreciate there are software tools that would make this ...
918 views

Render with camera perspective off-center

So ordinarily we have this But I'm after this! Is it possible to do this? Ideally by changing the projection matrix? The reasoning is kinda interesting - I am developing for mobile VR, and I have ...
185 views

Solving a problem from *Foundations of Computer Graphics*:

From Gortler's Foundations of Computer Graphics (i.e., self-study): Let $\mathbf{\vec{e}}^t = \mathbf{\vec{w}}^t E$ and let $P$ be a camera matrix that is just some arbitrary $4$ by $4$ matrix with ...
350 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 ...
141 views

Image based lighting, tangent space coordinates, and optimization

When I saw an implementation of normal mapping that computed the TBN matrix in the vertex shader and converted everything (in particular the view vector and light vector) to tangent space at that ...
155 views

How to get polygon coordinates in screen space

I need to be able to click on this polygon in 2d. This polygons set of vertices aren't in the same space as the screen. (Ie: the edge of the screen may be a value of 20 in one space but 1920 in the ...
523 views

Inverse value in a Perspective Matrix

I am a new leaner of computer graphics. I'm trying to understand a code I found online and I got stuck in the following formula: ...
462 views

What does it *mean* to scale in an arbitrary direction?

My graphics text explains rotating along the cardinal axes, then generalizes the math to show how to make a rotation matrix for rotating around an arbitrary vector. That all makes sense and I can both ...
62 views

Modulo vs Scaling vs Capping when performing filters

I'm currently taking a graphics course and we've recently covered cross-correlation with regards to using a filter matrix that is applied to a region of pixels in a sort of continual raster-type scan ...
121 views

Correctness of logical steps for create the matrix of viewing transformation

In general, I understand the creation of viewing transformation matrix, but I have my doubts. For example, let's say that a world coordinate (called $A$) has a center at $(1,1,1)$, and the view ...
1k views

Unable to pass custom Matrix4 to GLSL as a uniform

I am fairly new to graphics programming and I am trying to pass a custom Matrix4 (non-glm) to my vertex shader by using a uniform. ...
836 views

row and column majored rotation matrix pre- or post- multiplied

For column-major rotation matrices (right up forward in columns) do you right-multiply (post-multiply?) a row vector or left-multiply (pre-multiply) a column vector to result in a correct/valid ...
497 views

Rotation matrix for a 3D object in space

This is the follow-up question from here: Minimum requirements to uniquely represent a 3D object in space Assume I have 3 original points in a 3D object (in 3D space) as ...
218 views

View Reference Coordinate System

For a 3D scene in the World Coordinates, its View Reference Point is at c=(0,3,4), and a viewer is looking towards its origin O (0,0,0). Construct a transform matrix which will map World Coordinate ...
789 views

Why do we multiply vertex from left side in vertex shader with matrices?

I have been learning OpenGL 3.3 and I saw this expression: gl_Position = projection * view * model * vertex I am confused because I read in some book that if the ...
667 views

Correct view-space transform

I am attempting to model a simple graphics pipeline (i.e. Local->Word->View->Screen->2D spaces). I've been looking at the algorithm required to transform from world to view-space and using the ...
341 views

What's a parent vector space or coordinate system?

After asking this question, a few new terms that I had never heard of came up. Note, I'm quite familiar with linear algebra, but I've never heard these terms in the context of linear algebra. ...
754 views

3D rotation matrix around vector

I am using matrix for performing 3D rotations. I know that in 3D space the matrix product order is important - changing the order of the matrices can effect the rotate result. So I am interesting ...
209 views

Affine Transformation

We have a matrix $$\begin{bmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{bmatrix}$$ This matrix represents a ...
164 views

Why does opengl use 4d matrices for everything?

What I managed to figure out is that the first 3*3 is used for rotation and scale and the 1*3 at the end is used for position, but what is the bottom row used for? is it only for clipping related ...
194 views

Detect a lossy matrix decomposition?

I am writing a plugin to export data from 3DS Max. 3DS Max's geometry pipeline is... interesting. As part of my plugin I decompose a transform matrix into a translation, (quaternion) rotation & ...
113 views

Ladder to DNA using Transformation Matrix

In my last Graphic mid-term, the exam contained a Transformation Matrices problem, its statement was: Question Rotate the following ladder to form a DNA-shaped ladder using a transformation matrix....
510 views

Object rotating around origin instead of object center?

I am implementing simple rotation but the object is not rotating around the local center instead it is rotating around world origin. This is the code: ...
1k views

Inverse-Transpose of Vertex Normals

For the past month, I have been learning on my own and writing a little graphics library and am currently working on the transformation of vertex normals to soon support lighting/shading. I understand ...
586 views

Choosing & Using a Projection Matrix

I'm looking into the graphics pipeline processes and at the moment in particular, perspective projection matrices. After looking in several different sources, and across the breadth of previous ...
353 views

Rotating an Object Around an Axis

I have a circular shape object, which I want to rotate like a fan along it's own axis. I can change the rotation in any direction i.e. dx, dy, dz using my transformation matrix. The following it's ...
130 views

Inverse matrix order of operation

If I have a rotation, $A$, and a translation, $B$, which I multiply like so $C = AB$ Does the inverse of $C$ not only inverse the magnitudes of $A$ and $B$ but also become the reverse of operations? ...
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 ...
4k views

How to derive a perspective projection matrix from its components?

This has been haunting me for several days now. I want to find the component that makes up of this 4x4 perspective projection matrix, with $l$(left), $r$(right), $b$(bottom), $t$(top), $n$(near), $f$(...
59 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 ...
689 views

Building view transform matrices

For a 3D scene in the world coordinates, its View Reference Point $\mathrm{VRP}$ is at $(5,-2,1)$, and a viewer is looking towards point $A=(1,1,1)$. Construct a transform matrix which will map world ...
3k views

Correcting my “look-at” matrix so that it works on non-camera objects?

I'm familiar with the "look-at" matrix and the goal of being able to rotate a Camera at a specific location towards a specified target. When I tell the ...
1k views

How to decompose projection matrix?

I want to decompose projection matrices into near, far, top, bottom, left and right values to create a bounding box for view frustum. I used the formula described in this site Decompose the OpenGL ...
220 views

Coordinate system transformation in motion capture files

I am trying to align two motion capture files from different sources. The motion capture file consist of a skeleton specified as a hierarchy of joints. Each joint i.e. "shoulder" has three pieces of ...
72 views

Do I need a normal matrix if I calculate lighting in an objects space?

As a quick reminder, here is what normal matrix is and why do we need it. Now the question - if I take the light position and transform it into an object space than I don't need the normal matrix at ...
55 views

Camera position in vertex shader

in the vertex shader I have the vertex position vpos which is in object space and I want to get the vector going from the camera to ...
54 views

Why inverse of an allignment matrix is the same as its transpose?

$A_{v}^{-1}$ = $A_{v}^{T}$ $A_{v}$ = Allignment matrix that alligns vector v with z axis $=$\begin{bmatrix} \frac{\lambda}{|v|} & \frac{-ab}{\lambda|v|} & \frac{-ac}{\lambda|v|} &...
64 views

Finding all possible reflection matrices for a given Wythoff construction

As a pet project, I'm trying to build a small app that visualizes 4D polytopes. I want to use the Wythoff Construction method, where the shape is generated kaleidoscopically by the interaction of 4 ...
259 views

Translate an arcball camera upwards or left-right

This problem is giving me a really hard time. I'm always looking at the origin and have a camera that moves around it in an arcball mode. That part works beautifully: I'm calculating the camera ...
2k views

Screen space coordinates to Eye space conversion

I'm trying to figure out how to reverse Eye space -> projection -> clip(divide by w) -> screen space conversion. Basically, I want to get Screen space (still have z value for z-buffer) -> undivide? ...
46 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 ...