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Questions tagged [linear-algebra]

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3
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0answers
29 views

NURBS Weights De Boor's Algorithm

I am having trouble implementing an algorithm for 3rd degree NURBS. I have been able to program 2nd degree ones from the equations described here but I am not able to derive an equation for Rational B-...
1
vote
3answers
215 views

How to calculate ray

In ray-tracing technique critical point is to calculate rays which came out from eye $E$ to target $T$ through pixel $P_{ij}$ on viewport. The "viewport" is represented as rectangle divided to square ...
2
votes
1answer
122 views

Project vertex onto plane

What I have: a plane given by its normal$\ n $ and a point on the plane$\ p $. a 3D-point$\ v $. a direction$\ d$. What I need: the projection of$\ v$ along$\ d$ onto the plane. How can I ...
1
vote
1answer
88 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 ...
0
votes
0answers
102 views

Changing coordinate system from texelFetch to textureLod is breaking the algebra

I have a scene rendered using texelFetch() and I am trying to modify the shader to use textureLod() instead. This is the image generated with texelFetch: When I try to change the shader to use ...
0
votes
1answer
131 views

Skeletal animation: What is the purpose of multiplying interpolated bone matrix with parent's matrix?

Let's say I have the following hierarchy: Bone A Bone B Bone C Here's how most tutorial is telling me how to calculate the finalMatrix to be sent to ...
1
vote
1answer
315 views

Confusion about how inverse bind pose is actually calculated and used?

I am trying to do skeletal animation using Assimp and the inverse bind pose matrix just trips me up. I will give a little example to illustrate my point. ...
2
votes
1answer
2k 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), $f$(...
5
votes
1answer
278 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 ...
4
votes
1answer
134 views

Why does an affine transform work only on three of the corners?

I am trying to use a linear transformation to straighten out the camera angle on this image: In other words, I want to transform the image into a head-on view of the whiteboard. I applied an affine ...
1
vote
0answers
355 views

360 degrees rotation around x axis

How do we rotate the camera around x axis 360 degrees, without having to flip the axis, meaning without having the strange flip after we go over +-90 degrees on <...
3
votes
1answer
113 views

pseudoinverse Jacobian and adding more control in computer animation

I am studying inverse kinematics. But I wonder the suggested equations. (The following equations are taken from 'Computer Animation Algorithms and Techniques Third Edition Page, 181') To better ...
4
votes
1answer
329 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 ...
1
vote
1answer
268 views

Final transformation matrix to transform world coordinate into vrc [duplicate]

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 ...
2
votes
1answer
627 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 ...