Computer Graphics Stack Exchange
Computer Graphics Stack Exchange

Questions tagged [mathematics]

The knowledge of the numbers, formulas, shapes and quantities. In the computer graphics, almost exclusively linear algebra is being used.

209 questions
14
votes
1 answer

Thorough, accessible material about Fourier basis functions and Spherical Harmonics?

Spherical harmonics appear in several computer graphics techniques. I feel that in order to be a better computer graphics developer, I need to have a deep understanding of what they are and how they are used. It seems that the reference most often…
wip
  • 1,851
  • 1
  • 13
  • 26
4
votes
1 answer

Understanding distinct vs. not distinct knots in B-splines

In reading the wikipedia page about B-Splines https://en.wikipedia.org/wiki/B-spline, I am getting confused about the concept of knots. If we have a spline of order $n$, with a knot vector ($t_0, \cdots, t_k$), then if the $k$ knots are distinct, I…
IntegrateThis
  • 155
  • 5
4
votes
2 answers

Barycentric coordinates for 5-sided polytope of two triangles and three trapezoids

I have a triangle that is extended in space and each edge is refracted differently, creating a 5 sided polytope. The initial and final triangles are the view radii segments of a frustum. We need to get the u and v along the triangle and the w depth…
user5884
  • 53
  • 3
4
votes
2 answers

Why is $pdf(\Psi) = \frac{1}{2\pi}$ when picking from hemisphere uniformly?

I'm trying to figure out why the probability density function for picking a direction uniformly on the hemisphere is $\frac{1}{2\pi}$. Something tells me this is related to the number of steradians in a hemisphere being $2\pi$, but I can't see how…
PeteUK
  • 700
  • 5
  • 13
4
votes
2 answers

Degree for Computer Graphics : Computer Science or Mathematics?

I want to learn graphics on a lower level but I have no clue where to start. I know that I will need some hard mathematics (linear algebra, vectors, matrices, transformations...) rooted inside my head. Would it be a viable and better pathway to…
Vie Infernal
  • 41
  • 3
3
votes
1 answer

Fastest way to put a point on the circumference of a circle

My goal is to take a point that is inside of a circle with a given radius and put it on the circumference. Recently I have been normalizing the vector between the point and the center of the circle then multiplying that by the radius. However I…
J.Doe
  • 1,445
  • 12
  • 23
2
votes
1 answer

How can I draw regular polygons along the horizontal axis?

I drew simple triangle wave (that you can see It on graph toy). f1(x) = frac(x/(PI+5))*(PI+5) f2(x) = frac(-x/(PI+5))*(PI+5) f3(x) = min(f1(x),f2(x))*1.5 I want to change above shape like Approximating Pi and repeat It periodically along…
Seyed Morteza Kamali
  • 323
  • 2
  • 12
2
votes
0 answers

Line segment intersection test and find the point of intersection

Thanks for the suggestions. Now I am doing it as follows: First off it is identified if two line segments intersect or not. And I am using the algorithm described in the book - "Introduction to Algorithms" chapter 33 (Computational Geometry). int…
sajis997
  • 1,279
  • 1
  • 10
  • 15
1
vote
0 answers

Hashing a point on cubic sphere

Let's say I have a point on a potential cubic sphere inflated using this: Vector3 v = new Vector3(x, y, z) * 2f / gridSize - Vector3.one; float x2 = v.x * v.x; float y2 = v.y * v.y; float z2 = v.z * v.z; Vector3 s; s.x = v.x * Mathf.Sqrt(1f - y2 /…
user29244
  • 121
  • 2
1
vote
2 answers

How to find vertices on borders of geometry

I trying to highlight vertices which are on "borders", imagine half of sphere for example. Also for example I added image geomtry with triangles and highlighted necessary vertices. Any ideas? Thanks
Nikita Krupitskas
  • 21
  • 2
1
vote
1 answer

Enter/Exit of unit cube representable as 4 numbers?

In the paper Real-time Reflection using Ray Tracing with Geometry Field , it mentions this: A ray is represented by its two intersection points (in,out) with the bounding box of the surface. Hence, the geometry field is a 4 dimensional …
Alan Wolfe
  • 7,801
  • 3
  • 30
  • 76
0
votes
0 answers

What are some uses for the vector triple product in computer graphics?

I have just learned about the vector triple product (Lagrange formula) from a math for computer graphics textbook, however the book does not mention any use cases for it beyond the fact that it's a simpler way to say: cross(a,cross(b,c) ==…
mbl
  • 291
  • 1
  • 8
0
votes
0 answers

How to derive the formula@NathanReed answer

Thanks! A very simple but great way to estimate mean curvatures@NathanReed answer. For my case, I also need an estimate of triangular mesh curvature, and I support this is what i was looking for. However, could you please show me (or any recommended…
H. Wang
  • 1
  • 1
0
votes
0 answers

Explanation of converting a look-at / direction vector to quaternion rotation?

Can someone please explain the math behind converting a direction-vector or lookAt-vector into a quaternion rotation? What I am trying to do? I am trying to create a custom aim-constraint for a DCC (Maya. Also, Maya already provides one but I have…
user2259784
  • 101
  • 2