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tetris.cpp
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tetris.cpp
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#include "taichi.h" // Note: You DO NOT have to install taichi or taichi_mpm.
using namespace taichi; // You only need [taichi.h] - see below for
// instructions.
const int n = 160 /*grid resolution (cells)*/, window_size = 800;
const real dt = 60e-4_f / n, frame_dt = 1e-3_f, dx = 1.0_f / n,
inv_dx = 1.0_f / dx;
auto particle_mass = 1.0_f, vol = 1.0_f;
auto hardening = 10.0_f, E = 1e4_f, nu = 0.2_f;
real mu_0 = E / (2 * (1 + nu)), lambda_0 = E * nu / ((1 + nu) * (1 - 2 * nu));
using Vec = Vector2;
using Mat = Matrix2;
struct Particle {
Vec x, v;
Mat F, C;
real Jp;
int c /*color*/;
int type; // 0: elastic 1: plastic 2: liquid
Particle(Vec x, int c, int type, Vec v = Vec(0))
: x(x), v(v), F(1), C(0), Jp(1), c(c), type(type) {
}
};
std::vector<Particle> particles;
Vector3 grid[n + 1][n + 1]; // velocity + mass, node_res = cell_res + 1
// http://zetcode.com/tutorials/javaswingtutorial/thetetrisgame/
int tetris_offsets[7][3][2] = {
// excluding center
{{0, -1}, {1, 0}, {0, -2}}, {{1, 1}, {-1, 0}, {1, 0}},
{{0, -1}, {-1, 0}, {0, -2}}, {{0, 1}, {1, 0}, {1, -1}},
{{1, 0}, {2, 0}, {-1, 0}}, {{0, 1}, {1, 1}, {1, 1}},
{{-1, 0}, {1, 0}, {0, 1}}};
void advance(real dt) {
std::memset(grid, 0, sizeof(grid)); // Reset grid
for (auto &p : particles) { // P2G
Vector2i base_coord =
(p.x * inv_dx - Vec(0.5_f)).cast<int>(); // element-wise floor
Vec fx = p.x * inv_dx - base_coord.cast<real>();
// Quadratic kernels [http://mpm.graphics Eqn. 123, with x=fx, fx-1,fx-2]
Vec w[3]{Vec(0.5) * sqr(Vec(1.5) - fx), Vec(0.75) - sqr(fx - Vec(1.0)),
Vec(0.5) * sqr(fx - Vec(0.5))};
auto e = std::exp(hardening * (1.0_f - p.Jp)), mu = mu_0 * e,
lambda = lambda_0 * e;
real J = determinant(p.F); // Current volume
Mat r, s;
polar_decomp(p.F, r, s); // Polar decomp. for fixed corotated model
Mat cauchy;
if (p.type == 2) {
cauchy = Mat(0.2_f * E * (pow<1>(p.Jp) - 1));
} else {
cauchy = 2 * mu * (p.F - r) * transposed(p.F) + lambda * (J - 1) * J;
}
auto stress = // Cauchy stress times dt and inv_dx
-4 * inv_dx * inv_dx * dt * vol * cauchy;
auto affine = stress + particle_mass * p.C;
for (int i = 0; i < 3; i++)
for (int j = 0; j < 3; j++) { // Scatter to grid
auto dpos = (Vec(i, j) - fx) * dx;
Vector3 mv(p.v * particle_mass,
particle_mass); // translational momentum
grid[base_coord.x + i][base_coord.y + j] +=
w[i].x * w[j].y * (mv + Vector3(affine * dpos, 0));
}
}
for (int i = 0; i <= n; i++)
for (int j = 0; j <= n; j++) { // For all grid nodes
auto &g = grid[i][j];
if (g[2] > 0) { // No need for epsilon here
g /= g[2]; // Normalize by mass
g += dt * Vector3(0, -200, 0); // Gravity
real boundary = 0.05, x = (real)i / n,
y = real(j) / n; // boundary thick.,node coord
if (x < boundary || x > 1 - boundary || y > 1 - boundary)
g = Vector3(0); // Sticky
if (y < boundary)
g[1] = std::max(0.0_f, g[1]); //"Separate"
}
}
for (auto &p : particles) { // Grid to particle
Vector2i base_coord =
(p.x * inv_dx - Vec(0.5_f)).cast<int>(); // element-wise floor
Vec fx = p.x * inv_dx - base_coord.cast<real>();
Vec w[3]{Vec(0.5) * sqr(Vec(1.5) - fx), Vec(0.75) - sqr(fx - Vec(1.0)),
Vec(0.5) * sqr(fx - Vec(0.5))};
p.C = Mat(0);
p.v = Vec(0);
for (int i = 0; i < 3; i++)
for (int j = 0; j < 3; j++) {
auto dpos = (Vec(i, j) - fx),
grid_v = Vec(grid[base_coord.x + i][base_coord.y + j]);
auto weight = w[i].x * w[j].y;
p.v += weight * grid_v; // Velocity
p.C +=
4 * inv_dx * Mat::outer_product(weight * grid_v, dpos); // APIC C
}
p.x += dt * p.v; // Advection
if (p.type <= 1) { // plastic
auto F = (Mat(1) + dt * p.C) * p.F; // MLS-MPM F-update
if (p.type == 1) {
Mat svd_u, sig, svd_v;
svd(F, svd_u, sig, svd_v);
for (int i = 0; i < 2; i++) // Snow Plasticity
sig[i][i] = clamp(sig[i][i], 1.0_f - 2.5e-2_f, 1.0_f + 7.5e-3_f);
real oldJ = determinant(F);
F = svd_u * sig * transposed(svd_v);
real Jp_new = clamp(p.Jp * oldJ / determinant(F), 0.6_f, 20.0_f);
p.Jp = Jp_new;
}
p.F = F;
} else { // liquid
p.Jp *= determinant(Mat(1) + dt * p.C);
}
}
}
void add_object(Vec center, int type, int block) {
auto gen = [&](int k) {
Vector2 offset(0, 0);
if (k >= 0)
offset =
Vector2(tetris_offsets[block][k][0], tetris_offsets[block][k][1]);
int colors[] {0xED553B, 0xF2B134, 0x068587};
for (int i = 0; i < 30 * pow<2>(n / 80.0); i++)
particles.push_back(
Particle((Vec::rand() + offset) * 0.05_f + center, colors[type], type));
};
gen(-1);
gen(0);
gen(1);
gen(2);
}
int main() {
GUI gui("MLS-MPM Tetris", window_size, window_size);
for (int i = 0; i < 7; i++) {
add_object(Vector2(0.3 + i % 2 * 0.3, 0.2 + i * 0.08), i % 3, i);
}
auto &canvas = gui.get_canvas();
int f = 0;
for (int i = 0;; i++) { // Main Loop
advance(dt); // Advance simulation
if (i % int(frame_dt / dt) == 0) { // Visualize frame
canvas.clear(0x112F41); // Clear background
canvas.rect(Vec(0.04), Vec(0.96))
.radius(2)
.color(0x4FB99F)
.close(); // Box
for (auto p : particles)
canvas.circle(p.x).radius(2).color(p.c); // Particles
gui.update(); // Update image
// canvas.img.write_as_image(fmt::format("tmp/{:05d}.png", f++));
}
}
} //----------------------------------------------------------------------------
// g++ tetris.cpp -std=c++14 -g -lX11 -lpthread -O3 -o tetris && ./tetris