Is it possible to model polar coordinates in WebGL - webgl

I want to convert a set of coordinates into polar coordinates (the easy part), and then model them on a polar 3D grid. Is this possible using WebGL or are only Cartesian coordinates supported?

You can implement any type of coordinate transform you want in shaders. However, there is an important restriction:
If you draw two connected vertices (i.e. a straight line, or the edge of a triangle), the result will always be a straight line on the screen — it is not possible to do otherwise in OpenGL.
The Cartesian-polar transform turns straight lines into curved lines. This means that if you want to transform a straight-sided shape and get the “right” curved result, you must draw it using a sequence of closely-spaced vertices — as many as you need to produce the “resolution” of smooth curvature you want. This is generally not hard to program, but it is something to be aware of.

You can use shaders in webgl so you can give your inputs as polar coordinates and have webgl transform them to cartesian internally.

Related

WebGL: Draw different geometric primitives within same draw call?

I have a WebGL scene that wants to draw both point and line primitives, and am wondering: Is it possible to draw multiple WebGL primitives inside a single draw call?
My hunch is this is not possible, but WebGL is constantly surprising me with tricks one can do to accomplish strange edge cases, and searching has not let me confirm whether this is possible or not.
I'd be grateful for any insight others can offer on this question.
You can't draw WebGL lines, points, and triangles in the same draw call. You can generate points and lines from triangles and then just draw triangles in one draw call that happens to have triangles that make points and triangles that draw lines and triangles that draw other stuff all one draw call.
Not a good example but for fun here's a vertex shader than generates points and lines from triangles on the fly.
There's also this for an example of making lines from triangles
How creative you want to get with your shaders vs doing things on the CPU is up to you but it's common to draw lines with triangles as the previous article points out since WebGL lines can generally only be a single pixel thick.
It's also common to draw points with triangles since
WebGL is only required to support points of size 1
By drawing with triangles that limit is removed
WebGL points are always aligned with the screen
Triangle based points are far more flexible. You can rotate the point for example and or orient them in 3D. Here's a bunch of points made from triangles
Triangle based points can be scaled in 3D with no extra work
In other words a triangle based point in 3d space will scale with distance from the camera using standard 3D math. A WebGL point requires you to compute the size the point should be so you can set gl_PointSize and so requires extra work if you want it to scale with the scene.
It's not common to mix points, lines, and triangles in a single draw call but it's not impossible by any means.

Polygon(Quad) to Square Cells

I am really having a problem with this.
I have a polygon (a quad) which can be any shape. When my mouse is inside the polygon I need to find the x,y values of where my mouse is (inside the quad) as though the poygon were are perfect square. Further explanation; I have a 32x32 texture applied to the polygon and I need to know the x,y of the texture that the mouse is over.
I have some code that works for most shapes but which breaks if TR.Y is less than TL.y for instance.
I have some pretty simple code that tests whether the cursor is inside the polygon (via two triangle tests). But I cannot figure out how to use this to generate an x,y of a virtual square projection.
This problem is killing me. What is the name of operation i am trying to perform? Does anyone know of an explanation where the equations are presented in code form (any kind of code) (rather than just mathematical notation?). Any kind of help would be so appreciated.
I am on the verge of doing a 2nd render with specially formatted textures (each pixel having a unique value) so that I can just colour test to get an approximate x,y match (and precision is something that can be compromised here without causing too much trouble) - but then I will have to work around the DX Lib's attempt to blend and smooth the special texture as it is warped to fill the quad)
**Edit: Code that works for many quad shapes
It depends on method - how the texture is drawn at this quad.
If it uses perspective transform Square=>Quad, you have to use matrix of inverse transform Quad=>Square. Short article
For linear interpolation approach see this page

Draw line between two points (x1,y1,z1) to (x2,y2,z2)

I know how to draw line on 2d surface.But I can't find a way to draw a line in space.
I have wrote a demo
and now I want to draw line in space.
and finish it like this:
I have finished the 2d surface rotate in space use CATransform3D already. But I don't know how to draw line in space.
Thanks a lot.
Normal drawing on iOS is 2D. Core Animation is "2.5D", where it can draw flat images with fake 3D perspective. It doesn't let you "draw in space."
If you want real 3D perspective drawing you should use OpenGL, SceneKit, Metal, or some other 3D API.
Your trying to draw a 3d image on a 2d surface. Therefore you need some sort of mapping
https://en.m.wikipedia.org/wiki/3D_projection
Has some options for you. Orthographic projection is probably what you want though
https://upload.wikimedia.org/math/8/3/a/83a402b37056afa1dd4c8d706a9a2d75.png
Is the equation you would want to use where s is a scaling factor and c is an offset

Projective texture mapping in WebGL

I wrote two simple WebGL demos which use a 512x512 image as texture. But the result is not what I want. I know the solution is to use projective texture mapping(or any other solutions?) but I have no idea how to implement it in my simple demos. Anyone can help?
The results are as follows(both of them are incorrect):
Codes of demos are here: https://github.com/jiazheng/WebGL-Learning/tree/master/texture
note: Both the model and texture could not be modified in my case.
In order to get perspective-correct texture mapping, you must actually be using perspective. That is, instead of narrowing the top of your polygon along the x axis, move it backwards along the z axis, and apply a standard perspective projection matrix.
I'm a little hazy on the details myself, but my understanding is that the way the perspective matrix maps the z coordinate into the w coordinate is the key to getting the GPU to interpolate along the surface “correctly”.
If you have already-perspective-warped 2D geometry, then you will have to implement some method of restoring it to 3D data, computing appropriate z values. There is no way in WebGL to get a perspective quadrilateral, because the primitives are triangles and there is not enough information in three points to define the texture mapping you're looking for unambiguously — your code must use the four points to work out the corresponding depths. Unfortunately, I don't have enough grasp of the math to advise you on the details.
You must specify vec4 texture coordinates not vec2. The 4th field in each vec4 will be homogeneous w that when divided into x and y produce your desired coordinate. This in turn should allow the perspective correction division in hardware to give you a non affine mapping within the triangle provided your numbers are correct. Now, if you use a projection matrix to transform a vec4 with w=1 in your vertex shader you should get the correct vec4 numbers ready for perspective correction going into setup and rasterization for your fragment shader. If this is unclear then you need to seek out tutorials on projective texture transformation and homogeneous coordinates in projection.

Drawing a concave polygon in OpenGL

I have a concave polygon I need to draw in OpenGL.
The polygon is defined as a list of points which form its exterior ring, and a list of lists-of-points that define its interior rings (exclusion zones).
I can already deal with the exclusion zones, so a solution for how to draw a polygon without interior rings will be good too.
A solution with Boost.Geometry will be good, as I already use it heavily in my application.
I need this to work on the iPhone, namely OpenGL ES (the older version with fixed pipeline).
How can I do that?
Try OpenGL's tessellation facilities. You can use it to convert a complex polygon into a set of triangles, which you can render directly.
EDIT (in response to comment): OpenGL ES doesn't support tessellation functions. In this case, and if the polygon is static data, you could generate the tessellation offline using OpenGL on your desktop or notebook computer.
If the shape is dynamic, then you are out of luck with OpenGL ES. However, there are numerous libraries (e.g., CGAL) that will perform the same function.
It's a bit complicated, and resource-costly method, but any concave polygon can be drawn with the following steps (note this methos works surely on flat polygons, but I also assume you try to draw on flat surface, or in 2D orthogonal mode):
enable stencil test, use glStencilFunc(GL_ALWAYS,1,0xFFFF)
disable color mask to oprevent unwanted draws: glColorMask(0,0,0,0)
I think you have the vertices in an array of double, or in other form (strongly recommended as this method draws the same polygon multiple times, but using glList or glBegin-glEnd can be used as well)
set glStencilOp(GL_KEEP,GL_KEEP,GL_INCR)
draw the polygon as GL_TRIANGLE_FAN
Now on the stencil layer, you have bits set >0 where triangles of polygon were drawn. The trick is, that all the valid polygon area is filled with values having mod2=1, this is because the triangle fan drawing sweeps along polygon surface, and if the selected triangle has area outside the polygon, it will be drawn twice (once at the current sequence, then on next drawings when valid areas are drawn) This can happens many times, but in all cases, pixels outside the polygon are drawn even times, pixels inside are drawn odd times.
Some exceptions can happen, when order of pixels cause outside areas not to be drawn again. To filter these cases, the reverse directioned vertex array must be drawn (all these cases work properly when order is switched):
- set glStencilFunc(GL.GL_EQUAL,1,1) to prevent these errors happen in reverse direction (Can draw only areas inside the polygon drawn at first time, so errors happening in the other direction won't apperar, logically this generates the intersectoin of the two half-solution)
- draw polygon in reverse order, keeping glStencilFunc to increase sweeped pixel values
Now we have a correct stencil layer with pixel_value%2=1 where the pixel is truly inside the polygon. The last step is to draw the polygon itself:
- set glColorMask(1,1,1,1) to draw visible polygon
- keep glStencilFunc(GL_EQUAL,1,1) to draw the correct pixels
- draw polygon in the same mode (vertex arrays etc.), or if you draw without lighting/texturing, a single whole-screen-rectangle can be also drawn (faster than drawing all the vertices, and only the valid polygon pixels will be set)
If everything goes well, the polygon is correctly drawn, make sure that after this function you reset the stencil usage (stencil test) and/or clear stencil buffer if you also use it for another purpose.
Check out glues, which has tessellation functions that can handle concave polygons.
I wrote a java classe for a small graphical library that do exacly what you are looking for, you can check it here :
https://github.com/DzzD/TiGL/blob/main/android/src/fr/dzzd/tigl/PolygonTriangulate.java
It receive as input two float arrays (vertices & uvs) and return the same vertices and uvs reordered and ready to be drawn as a list of triangles.
If you want to exclude a zone (or many) you can simply connect your two polygones (the main one + the hole) in one by connecting them by a vertex, you will end with only one polygone that can be triangulate like any other with the same function.
Like this :
To better understand zoomed it will look like :
Finally it is just a single polygon.

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