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Author SHA1 Message Date
allem
d98a596a7b hopf fibration visualization - add arbitrary animations 2019-01-11 01:35:43 -05:00
2 changed files with 114 additions and 38 deletions
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2
simplex/shaders/main.vert
View File

@@ -12,5 +12,5 @@ out vec4 pos;
void main() {
pos = model * pos4;
gl_Position = proj * view * vec4(pos.xyz, -pos.w + 2);
gl_Position = proj * view * vec4(pos.xyz, 1);
}

150
simplex/src/main.cpp
View File

@@ -12,16 +12,51 @@
#include <glm/gtc/matrix_transform.hpp>
#include <glm/gtc/type_ptr.hpp>
#include <iostream>
#include <glm/ext.hpp>
#include <cstdlib>
#include <cstdio>
#include <vector>
#define PI 3.14159f
struct Matrices {
glm::mat4 model;
glm::mat4 view;
glm::mat4 proj;
};
void push_point(
std::vector<glm::vec4> &verts, std::vector<unsigned> &elems,
float xi_1, float xi_2, float eta) {
float x = cos((xi_2 + xi_1) / 2) * cos(eta);
float y = sin((xi_2 + xi_1) / 2) * cos(eta);
float z = cos((xi_2 - xi_1) / 2) * sin(eta);
float w = sin((xi_2 - xi_1) / 2) * sin(eta);
verts.emplace_back(x / (1 - w), y / (1 - w), z / (1 - w), w); // stereographic
// verts.emplace_back(x, y, z, w); // orthographic
}
void push_circle(
std::vector<glm::vec4> &verts, std::vector<unsigned> &elems,
float xi_1, float eta) {
const auto N = (unsigned) 128;
const auto R = (unsigned) verts.size();
for (unsigned k = 0; k < N; ++k) {
float xi_2 = 4 * PI * k / N;
push_point(verts, elems, xi_1, xi_2, eta);
elems.push_back(R + (k) % N);
elems.push_back(R + (k + 1) % N);
}
}
class GLApp : public App {
std::vector<glm::vec4> cell_verts{};
std::vector<unsigned> cell_elems{};
@@ -34,33 +69,51 @@ class GLApp : public App {
GLuint matrix_buffer{};
GLuint matrix_binding_point = 1;
void generate() {
cell_verts.clear();
cell_elems.clear();
// xi_1 from 0 to 2pi
// xi_2 from 0 to 4pi
// eta from 0 to pi/2
const unsigned M = 2;
const unsigned N = 32;
const float PAD = 0.025;
for (unsigned j = 0; j <= M; ++j) {
float eta = (PI / 2 - PAD * 2) * (1 + cos(getTime() / 6)) / 2 * j / M + PAD;
for (unsigned k = 0; k < N; ++k) {
float xi_1 = PI * 2 * k / N;
push_circle(cell_verts, cell_elems, xi_1, eta);
}
}
const unsigned O = 256;
for (unsigned k = 0; k < O; ++k) {
float t = (float) k / O;
int loops = 10;
float xi_1 = PI * 2 * (t + cos(loops * PI * t + getTime() / 6) / loops);
float eta =
sin(loops * PI * t) / loops + .5f + (cos(xi_1 + getTime() * 2) + cos(xi_1 + getTime() * 1.6f)) / 12;
push_circle(cell_verts, cell_elems, xi_1, eta);
}
glBindBuffer(GL_ARRAY_BUFFER, cell_vert_buf);
util::bufferData(GL_ARRAY_BUFFER, cell_verts, GL_STATIC_DRAW);
glBindBuffer(GL_ARRAY_BUFFER, 0);
glBindBuffer(GL_ELEMENT_ARRAY_BUFFER, cell_elem_arr_buf);
util::bufferData(GL_ELEMENT_ARRAY_BUFFER, cell_elems, GL_STATIC_DRAW);
glBindBuffer(GL_ELEMENT_ARRAY_BUFFER, 0);
}
void init() override {
cell_verts = {
glm::vec4(-0.5, -0.5, -0.5, -0.5),
glm::vec4(-0.5, -0.5, -0.5, +0.5),
glm::vec4(-0.5, -0.5, +0.5, -0.5),
glm::vec4(-0.5, -0.5, +0.5, +0.5),
glm::vec4(-0.5, +0.5, -0.5, -0.5),
glm::vec4(-0.5, +0.5, -0.5, +0.5),
glm::vec4(-0.5, +0.5, +0.5, -0.5),
glm::vec4(-0.5, +0.5, +0.5, +0.5),
glm::vec4(+0.5, -0.5, -0.5, -0.5),
glm::vec4(+0.5, -0.5, -0.5, +0.5),
glm::vec4(+0.5, -0.5, +0.5, -0.5),
glm::vec4(+0.5, -0.5, +0.5, +0.5),
glm::vec4(+0.5, +0.5, -0.5, -0.5),
glm::vec4(+0.5, +0.5, -0.5, +0.5),
glm::vec4(+0.5, +0.5, +0.5, -0.5),
glm::vec4(+0.5, +0.5, +0.5, +0.5),
};
cell_elems = {
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15,
0, 2, 4, 6, 8, 10, 12, 14, 1, 3, 5, 7, 9, 11, 13, 15,
0, 4, 8, 12, 1, 5, 9, 13, 2, 6, 10, 14, 3, 7, 11, 15,
0, 8, 1, 9, 2, 10, 3, 11, 4, 12, 5, 13, 6, 14, 7, 15,
};
matrices = {
glm::identity<glm::mat4>(),
glm::identity<glm::mat4>(),
@@ -77,14 +130,8 @@ class GLApp : public App {
//region Buffers
glGenBuffers(1, &cell_vert_buf);
glBindBuffer(GL_ARRAY_BUFFER, cell_vert_buf);
util::bufferData(GL_ARRAY_BUFFER, cell_verts, GL_STATIC_DRAW);
glBindBuffer(GL_ARRAY_BUFFER, 0);
glGenBuffers(1, &cell_elem_arr_buf);
glBindBuffer(GL_ELEMENT_ARRAY_BUFFER, cell_elem_arr_buf);
util::bufferData(GL_ELEMENT_ARRAY_BUFFER, cell_elems, GL_STATIC_DRAW);
glBindBuffer(GL_ELEMENT_ARRAY_BUFFER, 0);
glGenBuffers(1, &matrix_buffer);
glBindBufferBase(GL_UNIFORM_BUFFER, matrix_binding_point, matrix_buffer);
@@ -93,6 +140,8 @@ class GLApp : public App {
glBindBuffer(GL_UNIFORM_BUFFER, 0);
//endregion
generate();
//region Vertex Arrays
glGenVertexArrays(1, &cell_array);
glBindVertexArray(cell_array);
@@ -113,14 +162,21 @@ class GLApp : public App {
glfwGetFramebufferSize(getWindow(), &width, &height);
float ratio = (float) width / height;
matrices.model = rotor_yw(getTime() / 5) * rotor_xz(getTime() / 2);
// matrices.model = rotor_yw(getTime() / 5) * rotor_xz(getTime() / 2);
//
float t = getTime() / 5;
// matrices.view = glm::lookAt(glm::vec3(0, 0, 0), -glm::vec3(cos(t), sin(t), .25), glm::vec3(0, 0, 1));
matrices.view = glm::lookAt(glm::vec3(0, 0, -2), glm::vec3(0, 0, 0), glm::vec3(0, 1, 0));
matrices.proj = glm::perspective(1.f, ratio, 0.1f, 10.0f);
// matrices.proj = glm::perspective(1.f, ratio, 0.1f, 100.0f);
float W = 2;
float D = 10;
matrices.proj = glm::ortho(-ratio * W, ratio * W, -W, W, -D, D);
glBindBuffer(GL_UNIFORM_BUFFER, matrix_buffer);
glBufferSubData(GL_UNIFORM_BUFFER, 0, sizeof(Matrices), &matrices);
glBindBuffer(GL_UNIFORM_BUFFER, 0);
generate();
}
void display() override {
@@ -131,9 +187,9 @@ class GLApp : public App {
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
glPointSize(10);
glLineWidth(2);
glLineWidth(5);
glEnable(GL_DEPTH_BUFFER_BIT);
glEnable(GL_DEPTH_TEST);
glUseProgram(wire_prog);
glBindVertexArray(cell_array);
glDrawElements(GL_LINES, (GLsizei) cell_elems.size(), GL_UNSIGNED_INT, nullptr);
@@ -150,6 +206,26 @@ class GLApp : public App {
}
}
glm::vec3 euler{};
double x_ = 0, y_ = 0;
void onCursorPos(double x, double y) override {
auto dx = (float) (x - x_) / 100;
auto dy = (float) (y - y_) / 100;
if (glfwGetMouseButton(getWindow(), 0)) {
euler += glm::vec3(dy, 0, dx);
matrices.view = glm::identity<glm::mat4>();
matrices.view = glm::rotate(matrices.view, euler.x, glm::vec3(1, 0, 0));
matrices.view = glm::rotate(matrices.view, euler.y, glm::vec3(0, 1, 0));
matrices.view = glm::rotate(matrices.view, euler.z, glm::vec3(0, 0, 1));
}
x_ = x;
y_ = y;
}
public:
GLApp() : App(4, 4) {}
};