Why are there gaps in my fibonacci sphere?

None · 2023-06-22T17:50:15

I recently took an interest in sphere topologies to find which one is the best. The most popular one seems to be the fibonacci sphere, so I found some code from here https://stackoverflow.com/questions/9600801/evenly-distributing-n-points-on-a-sphere/26127012#26127012 and then ran it through an AI to convert the code to C and then do some optimizations #include <math.h> #include <stdio.h> #define MAX_POINTS 1000 void fibonacci_sphere(int samples, float points[][3]) { /* Generates points on a sphere using Fibonacci spiral sampling. :param samples: Number of points to generate. :type samples: int :param points: Array to store generated points. :type points: list of lists :raises TypeError: If samples is not an integer or points is not a list of lists. :return: None */ // Validate inputs if (samples <= 0) { printf("Number of samples must be a positive integer.\n"); return; } if (points == NULL) { printf("Points array cannot be NULL.\n"); return; } // Calculate golden angle in radians float phi = M_PI * (sqrtf(5.0) + 1.0); // Generate points on sphere for (int i = 0; i < samples; i++) { // Calculate y coordinate float y = 1.0 - ((float)i / (float)(samples - 1)) * 2.0; // Calculate radius at y float radius = sqrtf(1.0 - y * y); // Calculate golden angle increment float theta = phi * i; // Calculate x, y, and z coordinates of point float x = cosf(theta) * radius; float z = sinf(theta) * radius; // Store point in points array points[i][0] = x; points[i][1] = y; points[i][2] = z; } // Log number of points generated printf("%d points generated on sphere.\n", samples); } which then outputs this Unnormalized vertices Unnormalized vertices (wireframe) And as you can see, these are unorganized right now, but when I normalize the vertices, I get this Normalized vertices Unnormalized vertices (wireframe) It is a sphere, but it's a little uneven, and plus there is a major gap down the middle, with a bunch of triangles stacking on top of each other unnecessarily. Here's the rest of my relevant code, starting with the application of the Fibonacci function, and then my tessellation shaders float vertices[100][3]; fibonacci_sphere(100, vertices); unsigned int vbo, vao; glGenVertexArrays(1, &vao); glGenBuffers(1, &vbo); glBindVertexArray(vao); // upload vertex data to gpu glBindBuffer(GL_ARRAY_BUFFER, vbo); glBufferData(GL_ARRAY_BUFFER, sizeof(vertices) * sizeof(double), &vertices[0], GL_STATIC_DRAW); // position attribute glVertexAttribPointer(0, 3, GL_FLOAT, GL_FALSE, 3 * sizeof(float), (void*)0); glEnableVertexAttribArray(0); // normal attribute glVertexAttribPointer(1, 3, GL_FLOAT, GL_FALSE, 3 * sizeof(float), (void*)(3 * sizeof(float))); glEnableVertexAttribArray(1); // amount of tessellation to do per triangle glPatchParameteri(GL_PATCH_VERTICES, 3); glBindVertexArray(vao); glDrawArrays(GL_PATCHES, 0, 100); #version 450 core // tessellation control // specify control points per output per patch // control size of input and output arrays layout(vertices=3) out; // input from vertex shader in vec3 vert_coord[]; // output to evaluation shader out vec3 vertex_coord[]; // for dynamic LOD (level of detail) uniform mat4 view; uniform mat4 model; void main() { // pass attributes through gl_out[gl_InvocationID].gl_Position = gl_in[gl_InvocationID].gl_Position; vertex_coord[gl_InvocationID] = vert_coord[gl_InvocationID]; // control tessellation if(gl_InvocationID==0) { // dynamic LOD (from the learnopengl.com website) // first: define rendering constants to control tessellation const float MIN_TESS_LEVEL = 4; const float MAX_TESS_LEVEL = 64; const float MIN_DISTANCE = 20; const float MAX_DISTANCE = 800; // second: transform each vertex into each eye vec4 eye_space_pos_1 = view * model * gl_in[0].gl_Position; vec4 eye_space_pos_2 = view * model * gl_in[1].gl_Position; vec4 eye_space_pos_3 = view * model * gl_in[2].gl_Position; // third: distance from camera scaled between 0 and 1 float distance_1 = clamp((abs(eye_space_pos_1.z)-MIN_DISTANCE)/(MAX_DISTANCE-MIN_DISTANCE), 0.0, 1.0); float distance_2 = clamp((abs(eye_space_pos_2.z)-MIN_DISTANCE)/(MAX_DISTANCE-MIN_DISTANCE), 0.0, 1.0); float distance_3 = clamp((abs(eye_space_pos_3.z)-MIN_DISTANCE)/(MAX_DISTANCE-MIN_DISTANCE), 0.0, 1.0); // fourth: interpolate edge tessellation level based on closer vertex float tess_level_1 = mix(MAX_TESS_LEVEL, MIN_TESS_LEVEL, min(distance_3, distance_1)); float tess_level_2 = mix(MAX_TESS_LEVEL, MIN_TESS_LEVEL, min(distance_1, distance_2)); float tess_level_3 = mix(MAX_TESS_LEVEL, MIN_TESS_LEVEL, min(distance_2, distance_1)); // fifth: set the corresponding outer tessellation levels gl_TessLevelOuter[0] = tess_level_1; gl_TessLevelOuter[1] = tess_level_2; gl_TessLevelOuter[2] = tess_level_3; // sixth: set the inner tessellation levels gl_TessLevelInner[0] = max(tess_level_2, tess_level_1); gl_TessLevelInner[1] = max(tess_level_1, tess_level_3); } } // tessellation evaluation #version 450 core // determines what type of tessellation to do layout(triangles, equal_spacing, cw) in; // input from control shader in vec3 vertex_coord[]; // output vec out vec3 vert; // allows for object transformations uniform mat4 model; uniform mat4 view; uniform mat4 projection; void main() { // gets barycentric coordinates from the triangles vec3 u = gl_TessCoord.x * vertex_coord[0]; vec3 v = gl_TessCoord.y * vertex_coord[1]; vec3 w = gl_TessCoord.z * vertex_coord[2]; // makes every triangle an equal distance from the center (that's how spheres are formed) vec3 pos = normalize(u + v + w); // output tessellated shape gl_Position = projection * view * model * vec4(pos, 1.0); }

Graphics and GPU Programming Programming

Started by Chillzy June 07, 2023 04:06 PM

13 comments, last by kwikc 1 year, 6 months ago

Chillzy

Author

June 21, 2023 02:21 PM

alvaro said:
To the OP: Did you figure out the problem? If you just render the vertices as a collection of dots, does it look right?

No, the problem is no longer the triangulation because I already found and implemented a working algorithm for that, the problem is I don't know what draw type to use, because I plotted out points, and then triangulated them, I would've thought that the problem was that I needed to draw with GL_TRIANGLES but that just draws the points I generated as triangles and doesn't give them algorithm a chance to triangulate them and leave the sphere as is. And of course, when I draw in GL_POINTS, it just draws the points I generated / plotted, so my problem is I don't know which draw type to properly display the data, or if I'm going to need to use some outside algorithm to help with that.

None

Aressera

3,172

June 21, 2023 04:39 PM

If it doesn't render correctly with GL_TRIANGLES, then your triangulation is wrong.

I'd recommend trying a different more practical sphere parametrization, such as the the quad sphere, which will make it much easier to generate the triangles, as well as easier to texture. You can get nearly even distribution of points on the sphere if you use the tan() function to warp the coordinates on each face.

Chillzy

Author

June 21, 2023 06:25 PM

@Aressera Yeah I just tested the algorithm a few more times, and I think the problem has to do with how I'm plotting the points, I'm going to try and plot the points top to bottom instead of from the side and see if that works. If it doesn't then I'll just try another way.

None