Back to posts.

# Mapping a texture on a disc

When you're using openGL and mapping a texture on a plain basic quad it is a quite trivial task. Though when the quad (two triangles) has a bit more tropical shape, it's not so obvious anymore. I ran into this problem when trying to map a texture onto a 2d disc. The shape onto which I wanted to map a texture looks like this:

When looking at this image it's directly obvious that the triangles are not nicely spread out over the disc and that the widths of the quads are different, when comparing the inner and outer segments.

When you map a texture onto a shape like this it will result in something like shown in the image below. Notice how much the texture gets distorted and you can clearly see the triangles.

Luckily there is a solution for this! The solution is similar to the way we do projective interpolation and is described in great detail on this page..

In short the solution to this, is to add a 3rd texture coordinate which is used to scale the interpolation. We call this extra texture coordinate `q`. The algorithms works like:

• Get the intersection point of the two diagonals of the quad
• Get the distance to this intersection point for each of the 4 points that make the quad
• Scale the texture coordinates according the formula as provided by the above link

On the CPU we calculate the q values (see linked post) and store those in a vertex attribute. Then we use this q value in the fragment shader to scale the texture coordinate.

### Calculate the `q` (and vertices of the ring)

The code below is a bit verbose to clarify the steps we take to calculate the `q` value. See below for a more concise example.

```void Mist::createRing(float x, float y, float radius, float width) {
offsets.push_back(vertices.size());

float resolution = 16.0;
float angle = TWO_PI/resolution;

for(int i = 0; i < resolution; ++i) {
float c0 = cos( (i + 0) * angle);
float s0 = sin( (i + 0) * angle);
float c1 = cos( (i + 1) * angle);
float s1 = sin( (i + 1) * angle);

// positions

// texcoords
float u0 = float(i+0)/resolution;
float u1 = float(i+1)/resolution;
vec3 ta(u0, 0.0f, 1.0f);
vec3 tb(u1, 0.0f, 1.0f);
vec3 tc(u1, 1.0f, 1.0f);
vec3 td(u0, 1.0f, 1.0f);

// calculate distances from the corners to the centers
vec3 intersection;
if(!intersect(pa, pc, pb, pd, intersection)) {
printf("The vertices of the dist do not intersect. Error.\n");
::exit(EXIT_FAILURE);
}

float d0 = length(pa - intersection);
float d1 = length(pb - intersection);
float d2 = length(pc - intersection);
float d3 = length(pd - intersection);

ta = ta * ((d0 + d2)/d2);
tb = tb * ((d1 + d3)/d3);
tc = tc * ((d2 + d0)/d0);
td = td * ((d3 + d1)/d1);

// store the vertices
VertexPT3 a(pa,ta);
VertexPT3 b(pb,tb);
VertexPT3 c(pc,tc);
VertexPT3 d(pd,td);

vertices.push_back(a);
vertices.push_back(b);
vertices.push_back(c);
vertices.push_back(a);
vertices.push_back(c);
vertices.push_back(d);
}

counts.push_back(vertices.size()-offsets.back());
needs_update = true;
}```

Another, shorter version of this was provided by Victor Martins:

```// From: http://www.reedbeta.com/blog/2012/05/26/quadrilateral-interpolation-part-1/
float off = fabsf(sinf(time*0.5f))*130.0f;
float3 verts[4];
float3 uvs[4];
float vertDistanceToCenter[4];

uvs[0].set( 0, 0, 1 );
uvs[1].set( 1, 0, 1 );
uvs[2].set( 1, 1, 1 );
uvs[3].set( 0, 1, 1 );

verts[0].set( 100, 100, 1 );
verts[1].set( 500, 100+off, 1 );
verts[2].set( 500, 500-off, 1 );
verts[3].set( 100, 500, 1 );

Segment s1( verts[0], verts[2] );
Segment s2( verts[1], verts[3] );

float3 intersectPoint = IntersectionLineLine2D( s1.p0, s1.p1, s2.p0, s2.p1 );
for( int i=0; i<4; i++ ) {
float dist = (intersectPoint - verts[i]).length();
vertDistanceToCenter[i] = dist;
}
for( int i=0; i<4; i++ ) {
int i2 = (i+2) % 4;
uvs[i] = uvs[i] * ( (vertDistanceToCenter[i] + vertDistanceToCenter[i2]) / vertDistanceToCenter[i2] );
}```

Then in the shader we scale the texture coordinate:

```// GLSL
vec4 diffuse_color = texture(u_tex, v_tex.xy / v_tex.z);```

The result is a lot better.

• NAT Types This is so exciting, in this article I dive into some of the different ways a NAT device translates addresses which is important for peer-to-peer connections.
• Building Cabinets In this post I dive into the design and construction of a cabinet with an interact LED strip. I also explain how I dynamically change the colors of the LEDs over TCP/UDP.
• Compiling GStreamer from source on Windows How to compile GStreamer on Windows from Source using Visual Studio 2019 and the meson build system.
• Debugging CMake Issues In this post I explain a process you can follow to debug issues with CMake by focusing on a specific target and making the output verbose.
• Dual Boot Arch Linux and Windows 10 How to install Arch Linux and Windows 10 Pro as dual boot. A step by step tutorial how to create bootable installers, partition and setup a dual boot menu.
• Mindset Updated Edition, Carol S. Dweck (Book Notes) Paragraphs I marked from the book "Mindset" from Carol S. Dweck.
• How to setup a self-hosted Unifi NVR with Arch Linux A step by step HOW-TO that explain show to setup a Unifi Video Controller with an NFS share with Arch Linux.
• Blender 2.8 How to use Transparent Textures Follow this node setup when you want to use an image with transparency as a "sticker".
• Compiling FFmpeg with X264 on Windows 10 using MSVC A couple of steps to compile FFmpeg on Windows using MSVC.
• Blender 2.8 OpenGL Buffer Exporter The following Blender script creates a [name].h and [name].cpp for the selected object and stores the positions, normals and UVs.
• Blender 2.8 Baking lightmaps Light maps are a cheap way to add a lot of realism to you static scenes and have been used forever.
• Blender 2.8 Tips and Tricks Use Environment Map only for reflections; create a floor plane for a Product Render, diffuse texture for roughness and more!
• Setting up a Bluetooth Headset on Arch Linux Learn how to setup a Sennheiser PXC 550 Bluetooth headset on Arch Linux.
• Compiling x264 on Windows with MSVC Compile the excellent x264 source on Windows using MSYS2 and MSVC.
• C/C++ Snippets Is a number divisible by four?
• Reading Chunks from a Buffer Some thoughts on reading bytes from a file; handy for reading NALs.
• Handy Bash Commands Bash scripts: removing white space, lowercase filenames, backup using tar, etc.
• Building a zero copy parser Simple solution to parse data in a pretty performant way. Used this for a RTSP protocol parser.
• Kalman Filter A very simple yet powerful filter which works great when you have to smooth noisy data. Used for the Nike Rise 2.0 project.
• Saving pixel data using libpng Do you have raw RGBA data that you want to save? Use this snippet to save it into a PNG file.
• Compile Apache, PHP and MySQL on Mac 10.10 Setup you own PHP, MySQL and Apache and with virtual document roots.
• Fast Pixel Transfers with Pixel Buffer Objects Using Pixel Buffer Objects (PBO) for fast asynchronous data transfers and OpenGL.
• High Resolution Timer function in C/C++ Wait...... wait.. fast high resolution timer funtions (Windows, Linux, Mac)
• Rendering text with Pango, Cairo and Freetype My never ending obsession with font rendering. A complex beast to do well. Use Pango and FreeType for the heavy lifting.
• Fast OpenGL blur shader Make things look blurry ... and fast using this OpenGL blur shader.
• Spherical Environment Mapping with OpenGL An old trick to get great lighting effects using Environment Maps and OpenGL.
• Using OpenSSL with memory BIOs OpenSSL is a great library with lots of abstractions. In this post I discuss how to break some of these abstractions and use your own memory buffers.
• Attributeless Vertex Shader with OpenGL A simple way to render a fullscreen quad without a vertex buffer with OpenGL.
• Circular Image Selector Some thoughts on a different way to select images from a huge collection in a compact UI.
• Decoding H264 and YUV420P playback Using libav to demux and playback with OpenGL.
• Fast Fourier Transform Analyse your audio using the Fastest Fourier Transform in the West.
• OpenGL Rim Shader Pretty glowy edges using a GLSL rim shader.
• Rendering The Depth Buffer Render the non-linear OpenGL Depth Buffer.
• Delaunay Triangulation Do you need to triangulate some shape: use the “Triangle” library.
• RapidXML RapidXML is a versatile and fast XML parser with a simple API. Check out these examples.
• Git Snippets Some simple GIT snippets; added here to remind myself.
• Basic Shading With OpenGL A couple of basic GLSL shaders with explanation.
• Open Source Libraries For Creative Coding Collection of great open source libraries for you creative programming projects.
• Bouncing particle effect Snippet that can be used to create a bouncy particle effect; basic, effective, simple but nice.
• OpenGL Instanced Rendering Want to render thousands and thousands of objects? Use OpenGL instanced rendering. The solution...the only solution.
• Mapping a texture on a disc Ever heard about projective interpolation related to texture mapping? Learn about this intertesting issue with OpenGL and texture mapping.
• Download HTML page using CURL When you want a quick solution to perform a HTTP(S) request CURL is always a quick an simple solution. Check out this example code.
• Height Field Simulation on GPU Although not a Navier-Stokes implementation ... still a very nice and enjoyable effect.
• OpenCV Optical Flow: when doing anything with tracking you've probably heard of it. See this simple example code using OpenCV and OpenGL.
• Some notes on OpenGL FBOs and Depth Testing, using different Attachment Points, a YUV420p shader, ...
• Math Meaning of the Dot Product in 3D graphics, calculating a perpendicular vector using Sam Hocevar's solution, orientation matrix and more.
• Gists to remember Some gists that I want to remember, often use, etc...
• Reverse SSH Do you want to login, into a remote PC but the remote PC is behind a firewall? Then use this simple reverse SSH trick which doesn't require changing your firewall rules.
• Working Set Having issues with your compiler? Or during linking? Check these common issues and their solutions. I also list several tools that you can use to get a some useful info.
• Consumer + Producer model with libuv Example of a common Multi Threaded Consumer/Producer Model using LibUV.
• Parsing binary data Learn about the basic of a binary protocol and how to create one easily yourself.
• C++ file operation snippets Reading a file into a string, vector, checking the file size, change to a position, etc. A collection of C++ file operation snippets.
• Importance of blur with image gradients Do you want to experiment with OpenGL and aligning Brush Strokes along Image Gradients? Then check out this post about the importance of blurring.
• Real-time oil painting with openGL Code snippet for fake "oil painting" effect with OpenGL using instanced rendering.
• x264 encoder Basic example on how to use libx264 to encode image data using libav
• Generative helix with openGL Screenshots of a project I worked on with that generates a DNA helix.
• Mini test with vector field Screenshots while experimenting with a vector field; nothing much to see here.
• Protractor gesture recognizer Testing the amazing One Dollar \$1 gesture recognizer. The simplest and very good gesture recognizer.
• Hair simulation Example code that implements the "Fast Simulation of Inextensible Hair and Fur" paper from M. Müller, T.Y. Kim and N.Chentanez.
• Some glitch screenshots Glitch screenshots.
• Working on video installation Screenshots of some experiments of a video installation.
• Generative meshes I enjoy creating physics based simulations and render them on high res. Here are some experiments I did a time ago.
• Converting video/audio using avconv Examples that show you how to use avconv to manipulate video and audio files.
• Auto start terminal app on mac Automatically start you application whe Mac boots and make sure that it restarts your app when it exists. Handy for interactive installations.
• Export blender object to simple file format Export the selected object in Blender into a .h and .cpp file that prepresents the buffer.