4 ms·

Beside the fact that the square fits the unit square and is not infinite at all, I'm not sure to get what you mean…

by mapio 9y ago

Robin_Message 9y ago
The u,v coordinates are infinite since an infinite number of copies fit in the unit square.
- ttoinou 9y ago
  Yes that's what I meant thx The same question goes Escher Infinite Circle. I know it has something to do with Poincaré Disk Model but can't figure it out
ttoinou 9y ago
If you draw a line from Point A to Point B, that's called Forward Drawing / Mapping. Basically you will loop over every sample that you know (thanks to a mathematical study) go near your line. The reverse would be to look at every sample you have and decides its colors based on the line information (the two points) with basic geometric calculus (distance of a point to a line). Applying anti-aliasing / thicks borders is more easy in this way also. The reverse is called Backward Drawing / Mapping, and is fit for GPU programming and others uses. Some problems are only defined for one kind of drawing and it's difficult to transform it to the other kind. It's like finding the inverse function of a mathematical function, hard.
- mapio 9y ago
  Sounds interesting… can you provide any reference? A technical/scientific paper, a book, a Wikipedia entry… I was unable to Google it using both "Backward Drawing" and "Backward Mapping" as keywords.
  - ttoinou 9y ago
    I learned "Forward Mapping" in a scientific paper when I was creating my own morphing and deformations algorithms, I don't remember which paper. (Some Googled links I just found : http://biomachina.org/courses/imageproc/051.pdf http://biomachina.org/courses/imageproc/051.pdf , https://www.cs.auckland.ac.nz/courses/compsci773s1c/lectures/ImageProcessing-html/topic2.htm https://www.cs.auckland.ac.nz/courses/compsci773s1c/lectures... ) The term is mainly used for image interpolation and GPU textures. I prefer to say "drawing" because the notion can be extended to anything you want to visualise. On the internet you can find a lot of visualization by forward drawing on a canvas. But recently there's more and more backward drawing with GPU and shaders (goto https://www.shadertoy.com/ https://www.shadertoy.com/ for a lot of examples)

Beside the fact that the square fits the unit square and is not infinite at all, I'm not sure to get what you mean…

by mapio 9y ago

Beside the fact that the square fits the unit square and is not infinite at all, I'm not sure to get what you mean…

Robin_Message 9y ago

The u,v coordinates are infinite since an infinite number of copies fit in the unit square.

ttoinou 9y ago
Yes that's what I meant thx The same question goes Escher Infinite Circle. I know it has something to do with Poincaré Disk Model but can't figure it out

ttoinou 9y ago

If you draw a line from Point A to Point B, that's called Forward Drawing / Mapping. Basically you will loop over every sample that you know (thanks to a mathematical study) go near your line. The reverse would be to look at every sample you have and decides its colors based on the line information (the two points) with basic geometric calculus (distance of a point to a line). Applying anti-aliasing / thicks borders is more easy in this way also. The reverse is called Backward Drawing / Mapping, and is fit for GPU programming and others uses. Some problems are only defined for one kind of drawing and it's difficult to transform it to the other kind. It's like finding the inverse function of a mathematical function, hard.

mapio 9y ago
Sounds interesting… can you provide any reference? A technical/scientific paper, a book, a Wikipedia entry… I was unable to Google it using both "Backward Drawing" and "Backward Mapping" as keywords.
- ttoinou 9y ago
  I learned "Forward Mapping" in a scientific paper when I was creating my own morphing and deformations algorithms, I don't remember which paper. (Some Googled links I just found : http://biomachina.org/courses/imageproc/051.pdf http://biomachina.org/courses/imageproc/051.pdf , https://www.cs.auckland.ac.nz/courses/compsci773s1c/lectures/ImageProcessing-html/topic2.htm https://www.cs.auckland.ac.nz/courses/compsci773s1c/lectures... ) The term is mainly used for image interpolation and GPU textures. I prefer to say "drawing" because the notion can be extended to anything you want to visualise. On the internet you can find a lot of visualization by forward drawing on a canvas. But recently there's more and more backward drawing with GPU and shaders (goto https://www.shadertoy.com/ https://www.shadertoy.com/ for a lot of examples)