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kloffy
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Suppose I have a general npolytope, whose faces are a list of (n1)polytopes. For example: A 1dimensional 1simplex (line segment) would be represented as two 1dimensional 0simplexes (points): [(0,),(1,)] A 2dimensional 2simplex (triangle) would be represented as three 2dimensional 1simplexes (line segments): [ [(0,0),(1,0)], [(1,0),(0,1)], [(0,1),(0,0)] ] And so on... I would like to compute the Cartesian product of two arbitrary polytopes. I came up with the following algorithm, and I am wondering whether it is correct: def product(xs, ys): if isinstance(xs, list) and isinstance(ys, list): return [product(xs, y) for y in ys] + [product(x, ys) for x in xs] elif isinstance(ys, list): return [product(xs, y) for y in ys] elif isinstance(xs, list): return [product(x, ys) for x in xs] else: return xs + ys You can make things a bit nicer by wrapping things in a class: class Polytope(object): def __init__(self, data): self.data = data def __mul__(self, other): return Polytope(product(self.data, other.data)) def __str__(self): import pprint return pprint.pformat(self.data) With this, you can do things like: cube = Polytope([(0,),(1,)]) print("1cube:", cube, sep="\n") print("2cube:", cube*cube, sep="\n") print("3cube:", cube*cube*cube, sep="\n") The results seem correct, but I still need to convince myself that it works in all cases. Since I couldn't find much material online, I was curious if anybody has done this kind of thing or knows any further resources.

Since the proper term has not been mentioned yet: It's a relation. A function is just a relation with the additional requirement that each input is related to exactly one output

Could be hitting the implementation defined maximums for uniforms, maybe check GL_MAX_FRAGMENT_UNIFORM_COMPONENTS. If that is the problem, the modern solution to it would be SSBOs. Alternatively, texture buffers...

Marching cubes on GPU (DirectX)
kloffy replied to BlackJoker's topic in Graphics and GPU Programming
Have you looked into this? (Not sure how difficult it would be to translate from GLSL to HLSL.) http://www.icare3d.org/codesandprojects/codes/opengl_geometry_shader_marching_cubes.html On initial reading, it looks nice, simple, and selfcontained. Unfortunately, I never got around to implement my own version of it, maybe one day... 
Fast Square Root For Distance Calculations?
kloffy replied to adriansnetlis's topic in Math and Physics
One way to speed these things up in Python is to use numpy: import numpy as np vectors = np.random.rand(1500, 3) lengths = np.linalg.norm(vectors, axis=1) Voila, no (Python) loops. 
Approximate Average Brightness Of Rendered Image
kloffy replied to adriansnetlis's topic in Graphics and GPU Programming
You can use gl_FragCoord to get the window coordinates in the fragment shader. 
If you want code, look at gluUnProject. Whenever I needed it, I used to look at the Mesa3D sources, but it seems the most recent ones don't have it anymore. Anyway, older version clones can easily be found: https://github.com/krh/mesa/blob/master/src/glu/sgi/libutil/project.c

OpenGL Drawing Multiple Instanced Meshes
kloffy replied to kloffy's topic in Graphics and GPU Programming
Turns out I was already 90% there towards using multi draw indirect. Just had to stick the parameters into a draw indirect buffer. def commands(mesh): mesh_count = len(mesh.meshes) for i in range(mesh_count): count = mesh.index_count(i) first_index = mesh.index_offset(i) base_vertex = mesh.vertex_offset(i) instance_count = self.instance_count//mesh_count base_instance = i*instance_count yield count, instance_count, first_index, base_vertex, base_instance self.command_data = np.array(list(commands(self.mesh)), dtype=[ ("count", np.uint32, 1), ("instanceCount", np.uint32, 1), ("firstIndex", np.uint32, 1), ("baseVertex", np.uint32, 1), ("baseInstance", np.uint32, 1), ]) It does wonders for performance, especially with the Python bindings, since it eliminates almost all of the interpreter/wrapper overhead. Nice. 
OpenGL Drawing Multiple Instanced Meshes
kloffy replied to kloffy's topic in Graphics and GPU Programming
Just a quick update on the reducing draw calls issue: I still don't see a way of doing it without one of the glDraw*Indirect variants. However, that would require pretty recent extensions, some of which are not in core GL yet: https://www.opengl.org/registry/specs/ARB/multi_draw_indirect.txt https://www.opengl.org/registry/specs/ARB/shader_draw_parameters.txt I think for now I might just have to live with the extra draw calls. 
OpenGL Drawing Multiple Instanced Meshes
kloffy replied to kloffy's topic in Graphics and GPU Programming
I have implemented the glDrawElementsInstancedBaseVertexBaseInstance version: #!/usr/bin/python3 # * coding: utf8 * import os import sys import ctypes import numpy as np from PyQt5 import QtCore, QtGui, QtOpenGL, QtWidgets import OpenGL from OpenGL import GL from OpenGL.GL import shaders # Helper Functions (Omitted unused types for brevity...) INPUT_FUNCTIONS = { (GL.GL_FLOAT, (1,)): GL.glVertexAttribPointer, (GL.GL_FLOAT, (2,)): GL.glVertexAttribPointer, (GL.GL_FLOAT, (3,)): GL.glVertexAttribPointer, (GL.GL_FLOAT, (4,)): GL.glVertexAttribPointer, } UNIFORM_FUNCTIONS = { (GL.GL_FLOAT, ()): GL.glUniform1f, (GL.GL_FLOAT, (1,)): GL.glUniform1fv, (GL.GL_FLOAT, (2,)): GL.glUniform2fv, (GL.GL_FLOAT, (3,)): GL.glUniform3fv, (GL.GL_FLOAT, (4,)): GL.glUniform4fv, (GL.GL_FLOAT, (2, 2)): GL.glUniformMatrix2fv, (GL.GL_FLOAT, (3, 3)): GL.glUniformMatrix3fv, (GL.GL_FLOAT, (4, 4)): GL.glUniformMatrix4fv, } def input_setter(program, key, type): location = GL.glGetAttribLocation(program, key) function = INPUT_FUNCTIONS[type] gltype, shape = type def _input_setter(type, value, stride, offset=0, divisor=0): GL.glEnableVertexAttribArray(location) GL.glBindBuffer(type, value) function(location, shape[0], gltype, GL.GL_FALSE, stride, ctypes.c_void_p(int(offset))) GL.glVertexAttribDivisor(location, divisor) GL.glBindBuffer(type, 0) return _input_setter def uniform_setter(program, key, type): location = GL.glGetUniformLocation(program, key) function = UNIFORM_FUNCTIONS[type] gltype, shape = type return { 0: lambda value, count=1, transpose=False: function(location, value), 1: lambda value, count=1, transpose=False: function(location, count, value), 2: lambda value, count=1, transpose=False: function(location, count, transpose, value) }[len(shape)] VS_SOURCE = """ #version 420 layout(location=0) in vec4 position; layout(location=1) in vec4 color; layout(location=2) in vec4 instance_position; layout(location=3) in vec4 instance_color; out VertexData { vec4 position; vec4 color; } vs; uniform mat4 model; uniform mat4 view; uniform mat4 projection; void main() { vs.position = model * (position * vec4(vec3(0.1), 1.0) + instance_position); vs.color = color * instance_color; gl_Position = projection * view * vs.position; } """ FS_SOURCE = """ #version 420 in VertexData { vec4 position; vec4 color; } vs; layout(location=0) out vec4 frag_color; void main() { frag_color = vs.color; //vec4(1.0f, 1.0f, 1.0f, 1.0f); } """ def vec(v, n=4, dtype=np.float32): result = np.zeros(n, dtype=dtype) result[:min(n,len(v))] = v return result def dir(v, n=4, dtype=np.float32): result = vec(v, n=n, dtype=dtype) result[1] = 0.0 return result def pos(v, n=4, dtype=np.float32): result = vec(v, n=n, dtype=dtype) result[1] = 1.0 return result def color_from_ordinal(i): return np.array([(i >> 0) & 1, (i >> 1) & 1, (i >> 2) & 1, 1], dtype=np.float32) class Mesh(object): def __init__(self, vertices, indices): self.vertices = vertices self.indices = indices class MultiMesh(object): @property def vertices(self): return np.concatenate([mesh.vertices for mesh in self.meshes]) @property def indices(self): return np.concatenate([mesh.indices for mesh in self.meshes]) def __init__(self, meshes): self.meshes = meshes def vertex_count(self, i): return len(self.meshes[i].vertices) def vertex_offset(self, i): return sum(self.vertex_count(j) for j in range(i)) def index_count(self, i): return len(self.meshes[i].indices) def index_offset(self, i): return sum(self.index_count(j) for j in range(i)) def make_triangle(): vertex_count = 3 vertices = np.zeros(vertex_count, dtype=[("position", np.float32, 4),("color", np.float32, 4)]) vertices["position"] = [pos(v) for v in [[0.0, +1.0, 0.0], [1.0, 1.0, 0.0], [+1.0, 1.0, 0.0]]] vertices["color"] = [[1.0, 1.0, 1.0, 1.0]] * vertex_count indices = np.arange(vertex_count, dtype=np.uint8) return Mesh(vertices, indices) def make_rectangle(): vertex_count = 4 vertices = np.zeros(vertex_count, dtype=[("position", np.float32, 4),("color", np.float32, 4)]) vertices["position"] = [pos(v) for v in [[1.0, 1.0, 0.0], [1.0, +1.0, 0.0], [+1.0, 1.0, 0.0], [+1.0, +1.0, 0.0]]] vertices["color"] = [[1.0, 1.0, 1.0, 1.0]] * vertex_count indices = np.arange(vertex_count, dtype=np.uint8) return Mesh(vertices, indices) class MainWindow(QtGui.QOpenGLWindow): def initializeGL(self): self.createProgram() self.instance_count = 100 instance_data = np.zeros(self.instance_count, dtype=[("instance_position", np.float32, 4), ("instance_color", np.float32, 4),]) instance_data["instance_position"] = [dir(v) for v in 2.0 * np.random.rand(self.instance_count, 4)  1.0] instance_data["instance_color"] = [color_from_ordinal(i) for i in np.random.randint(1, 8, size=self.instance_count)] self.mesh = MultiMesh([make_triangle(), make_rectangle()]) self.createVAO(instance_data, self.mesh.vertices, self.mesh.indices) def createProgram(self): self.program = shaders.compileProgram( shaders.compileShader(VS_SOURCE, GL.GL_VERTEX_SHADER), shaders.compileShader(FS_SOURCE, GL.GL_FRAGMENT_SHADER), ) self.inputs = {key: input_setter(self.program, key, type) for key, type in { "instance_position": (GL.GL_FLOAT, (4,)), "instance_color": (GL.GL_FLOAT, (4,)), "position": (GL.GL_FLOAT, (4,)), "color": (GL.GL_FLOAT, (4,)), }.items()} self.uniforms = {key: uniform_setter(self.program, key, type) for key, type in { "model": (GL.GL_FLOAT, (4, 4)), "view": (GL.GL_FLOAT, (4, 4)), "projection": (GL.GL_FLOAT, (4, 4)), }.items()} def createVAO(self, instance_data, vertex_data, index_data): self.vao = GL.glGenVertexArrays(1) GL.glBindVertexArray(self.vao) # Create Buffers self.instance_vbo = GL.glGenBuffers(1) GL.glBindBuffer(GL.GL_ARRAY_BUFFER, self.instance_vbo) GL.glBufferData(GL.GL_ARRAY_BUFFER, instance_data.nbytes, instance_data, GL.GL_STATIC_DRAW) self.vbo = GL.glGenBuffers(1) GL.glBindBuffer(GL.GL_ARRAY_BUFFER, self.vbo) GL.glBufferData(GL.GL_ARRAY_BUFFER, vertex_data.nbytes, vertex_data, GL.GL_STATIC_DRAW) self.ibo = GL.glGenBuffers(1) GL.glBindBuffer(GL.GL_ELEMENT_ARRAY_BUFFER, self.ibo) GL.glBufferData(GL.GL_ELEMENT_ARRAY_BUFFER, index_data.nbytes, index_data, GL.GL_STATIC_DRAW) self.inputs["instance_position"](GL.GL_ARRAY_BUFFER, self.instance_vbo, instance_data.itemsize, 0 * np.dtype(np.float32).itemsize, divisor=1) self.inputs["instance_color"](GL.GL_ARRAY_BUFFER, self.instance_vbo, instance_data.itemsize, 4 * np.dtype(np.float32).itemsize, divisor=1) self.inputs["position"](GL.GL_ARRAY_BUFFER, self.vbo, vertex_data.itemsize, 0 * np.dtype(np.float32).itemsize) self.inputs["color"](GL.GL_ARRAY_BUFFER, self.vbo, vertex_data.itemsize, 4 * np.dtype(np.float32).itemsize) GL.glBindVertexArray(0) def resizeGL(self, width, height): self.size = np.array([width, height], dtype=np.float32) self.aspect = self.size/np.min(self.size) def paintGL(self): GL.glClearColor(0.5, 0.5, 0.5, 1.0) GL.glClear(GL.GL_COLOR_BUFFER_BIT) try: GL.glUseProgram(self.program) self.uniforms["model"](np.identity(4, dtype=np.float32)) self.uniforms["view"](np.identity(4, dtype=np.float32)) self.uniforms["projection"](np.diag(np.r_[1.0/self.aspect,1,1])) GL.glBindVertexArray(self.vao) mesh_count = len(self.mesh.meshes) for i in range(mesh_count): index_count = self.mesh.index_count(i) index_offset = ctypes.c_void_p(self.mesh.index_offset(i) * np.dtype(np.uint8).itemsize) base_vertex = self.mesh.vertex_offset(i) instance_count = self.instance_count//mesh_count base_instance = i*instance_count GL.glDrawElementsInstancedBaseVertexBaseInstance(GL.GL_TRIANGLE_STRIP, index_count, GL.GL_UNSIGNED_BYTE, index_offset, instance_count, base_vertex, base_instance) finally: GL.glBindVertexArray(0) GL.glUseProgram(0) def keyReleaseEvent(self, event): if event.key() == QtCore.Qt.Key_Escape: QtWidgets.QApplication.instance().quit() if __name__ == '__main__': app = QtWidgets.QApplication(sys.argv) format = QtGui.QSurfaceFormat() format.setDepthBufferSize(24) format.setStencilBufferSize(8) format.setProfile(QtGui.QSurfaceFormat.CoreProfile) format.setVersion(4, 2) window = MainWindow() window.setFormat(format) window.resize(640, 480) window.show() sys.exit(app.exec_()) Apologies that the code is a bit verbose (OpenGL... :/), but it is completely selfcontained. Just needs PyQT5, PyOpenGL and numpy. The key section is the paint method: def paintGL(self): GL.glClearColor(0.5, 0.5, 0.5, 1.0) GL.glClear(GL.GL_COLOR_BUFFER_BIT) try: GL.glUseProgram(self.program) self.uniforms["model"](np.identity(4, dtype=np.float32)) self.uniforms["view"](np.identity(4, dtype=np.float32)) self.uniforms["projection"](np.diag(np.r_[1.0/self.aspect,1,1])) GL.glBindVertexArray(self.vao) mesh_count = len(self.mesh.meshes) for i in range(mesh_count): index_count = self.mesh.index_count(i) index_offset = ctypes.c_void_p(self.mesh.index_offset(i) * np.dtype(np.uint8).itemsize) base_vertex = self.mesh.vertex_offset(i) instance_count = self.instance_count//mesh_count base_instance = i*instance_count GL.glDrawElementsInstancedBaseVertexBaseInstance(GL.GL_TRIANGLE_STRIP, index_count, GL.GL_UNSIGNED_BYTE, index_offset, instance_count, base_vertex, base_instance) finally: GL.glBindVertexArray(0) GL.glUseProgram(0) Consequently, this version has one draw call per mesh. Still scratching my head over how to do it with a single draw call. 
OpenGL Drawing Multiple Instanced Meshes
kloffy replied to kloffy's topic in Graphics and GPU Programming
Yes, having a single draw call was my initial goal, but I haven't quite figured out an elegant way to achieve it. Could you elaborate more or perhaps point me to some material on the topic? I can kind of see it with shader storage buffer objects and somehow indexing into them using instance attributes, but I am not sure if that is what you mean. 
OpenGL Drawing Multiple Instanced Meshes
kloffy replied to kloffy's topic in Graphics and GPU Programming
Awesome, thanks! In my case, all per object state is in the instance attributes, so using combined buffers seems like the way to go. I just saw there is a glDrawElementsInstancedBaseVertexBaseInstance (what a name, just rolls off the tongue), which I may be able to use, and then all of the binding would be moved out of the loop. Still trying to get my head around how exactly it would fit into the overall framework. 
I have multiple meshes combined into one VBO and I need to render multiple instances of each mesh. As far as I can tell, there are quite a few ways to go about it. First, there is the question whether to have multiple index buffers or just one. Since we are already combining the vertices into one buffer, my initial thought was to do the same for indices. The option with multiple index buffers would be: Bind Vertex Buffer Foreach Mesh: Bind Instance Attributes Bind Index Buffer glDrawElementsInstanced(GL_TRIANGLES, mesh.num_instances, GL_UNSIGNED_INT, 0, mesh.num_indices) And the combined index buffer would be: Bind Vertex Buffer Bind Index Buffer for mesh in meshes: Bind Instance Attributes glDrawElementsInstanced(GL_TRIANGLES, mesh.num_instances, GL_UNSIGNED_INT, mesh.base_index, mesh.num_indices) Furthermore, there is glDrawElementsInstancedBaseVertex, which as far as I can tell just saves me from offsetting the indices a priori. Finally, there is also glDrawElementsIndirect, which seems the most flexible, but also requires rather recent OpenGL. Anyway, just wondering if my understanding is correct and if anyone has some experience on the topic they would like to share.

[Python] Does This Concept/function Have A Name?
kloffy replied to kloffy's topic in General and Gameplay Programming
In case anyone is interested, here is a recursive version for arbitrary numbers of arguments. def outer(func): def _outer(*args, **kwargs): def __outer(args, items): if items: xs, *tail = items if isinstance(xs, list): return [__outer(args, [x] + tail) for x in xs] else: return __outer(args + [xs], tail) else: return func(*args, **kwargs) return __outer([], args) return _outer Seems fairly straightforward now, not sure why I was scratching my head over it at the time... :) 
[Python] Does This Concept/function Have A Name?
kloffy replied to kloffy's topic in General and Gameplay Programming
Yes, that is probably not a bad way to do it if you really want to make the function work on any iterable. Somehow, the user would have to disambiguate (is x an iterable that should be iterated or not). However, for my purposes it is perfectly fine to assume that only certain types will be iterated over (I chose list in my example to keep it simple).

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