diff --git a/11_mpm_plastic/readme.md b/11_mpm_plastic/readme.md new file mode 100644 index 0000000..2a00dbd --- /dev/null +++ b/11_mpm_plastic/readme.md @@ -0,0 +1,15 @@ +# 2D Sand with a Sphere Collider + +A 2D sand block falling onto a static red sphere collider simulated by Material Point Method (MPM). The sand undergoes irreversible deformation and splashing upon impact, demonstrating granular flow and frictional boundary response. + +![results](results.gif) + +## Dependencies +``` +pip install numpy taichi +``` + +## Run +``` +python simulator.py +``` \ No newline at end of file diff --git a/11_mpm_plastic/results.gif b/11_mpm_plastic/results.gif new file mode 100644 index 0000000..76c3ab9 Binary files /dev/null and b/11_mpm_plastic/results.gif differ diff --git a/11_mpm_plastic/simulator.py b/11_mpm_plastic/simulator.py new file mode 100644 index 0000000..0a9fa3e --- /dev/null +++ b/11_mpm_plastic/simulator.py @@ -0,0 +1,279 @@ +# Material Point Method Simulation +import numpy as np # numpy for linear algebra +import taichi as ti # taichi for fast and parallelized computation + +ti.init(arch=ti.cpu) + +# sampling material particles with poisson-disk sampling +################################ +# Poisson Disk Sampling Tool +################################ +def poisson_disk_sampling(radius, domain_size, k=30): + """Bridson's algorithm for Poisson-disk sampling in 2D""" + cell_size = radius / np.sqrt(2) + grid_shape = (int(domain_size[0] / cell_size) + 1, int(domain_size[1] / cell_size) + 1) + grid = -np.ones(grid_shape, dtype=int) + samples = [] + active_list = [] + + def in_domain(p): + return 0 <= p[0] < domain_size[0] and 0 <= p[1] < domain_size[1] + + def get_cell_coords(p): + return int(p[0] / cell_size), int(p[1] / cell_size) + + def get_nearby_samples(p): + i, j = get_cell_coords(p) + neighbors = [] + for di in [-2, -1, 0, 1, 2]: + for dj in [-2, -1, 0, 1, 2]: + ni, nj = i + di, j + dj + if 0 <= ni < grid.shape[0] and 0 <= nj < grid.shape[1]: + idx = grid[ni, nj] + if idx != -1: + neighbors.append(samples[idx]) + return neighbors + + # Start with a random point + first_point = np.array([np.random.uniform(0, domain_size[0]), np.random.uniform(0, domain_size[1])]) + samples.append(first_point) + active_list.append(0) + grid[get_cell_coords(first_point)] = 0 + + while active_list: + idx = np.random.choice(active_list) + base_point = samples[idx] + found = False + for _ in range(k): + angle = np.random.uniform(0, 2 * np.pi) + r = np.random.uniform(radius, 2 * radius) + new_point = base_point + r * np.array([np.cos(angle), np.sin(angle)]) + if in_domain(new_point): + neighbors = get_nearby_samples(new_point) + if all(np.linalg.norm(new_point - n) >= radius for n in neighbors): + samples.append(new_point) + active_list.append(len(samples) - 1) + grid[get_cell_coords(new_point)] = len(samples) - 1 + found = True + if not found: + active_list.remove(idx) + return np.array(samples) + +# ANCHOR: data_def +# simulation setup +grid_size = 128 # background Eulerian grid's resolution, in 2D is [128, 128] +dx = 1.0 / grid_size # the domain size is [1m, 1m] in 2D, so dx for each cell is (1/128)m +dt = 2e-4 # time step size in second +ppc = 8 # average particle-per-cell + +density = 400 # kg / m^3 +E, nu = 3.537e5, 0.3 # sand's Young's modulus and Poisson's ratio +mu, lam = E / (2 * (1 + nu)), E * nu / ((1 + nu) * (1 - 2 * nu)) # sand's Lame parameters +sdf_friction = 0.5 # frictional coefficient of SDF boundary condition +friction_angle_in_degrees = 25.0 # Drucker Prager friction angle +# ANCHOR: D_def +D = (1./4.) * dx * dx # constant D for Quadratic B-spline used for APIC +# ANCHOR_END: D_def + +# sampling material particles with poisson-disk sampling +poisson_samples = poisson_disk_sampling(dx / np.sqrt(ppc), [0.2, 0.4]) # simulating a [30cm, 50cm] sand block + +# material particles data +N_particles = len(poisson_samples) +x = ti.Vector.field(2, float, N_particles) # the position of particles +x.from_numpy(np.array(poisson_samples) + [0.4, 0.55]) +v = ti.Vector.field(2, float, N_particles) # the velocity of particles +vol = ti.field(float, N_particles) # the volume of particle +vol.fill(0.2 * 0.4 / N_particles) # get the volume of each particle as V_rest / N_particles +m = ti.field(float, N_particles) # the mass of particle +m.fill(vol[0] * density) +F = ti.Matrix.field(2, 2, float, N_particles) # the deformation gradient of particles +F.from_numpy(np.tile(np.eye(2), (N_particles, 1, 1))) +C = ti.Matrix.field(2, 2, float, N_particles) # the affine-matrix of particles + +diff_log_J = ti.field(float, N_particles) # tracks changes in the log of the volume gained during extension + +# grid data +grid_m = ti.field(float, (grid_size, grid_size)) +grid_v = ti.Vector.field(2, float, (grid_size, grid_size)) +# ANCHOR_END: data_def + +# ANCHOR: reset_grid +def reset_grid(): + # after each transfer, the grid is reset + grid_m.fill(0) + grid_v.fill(0) +# ANCHOR_END: reset_grid + +################################ +# Stvk Hencky Elasticity +################################ +# ANCHOR: stvk +@ti.func +def StVK_Hencky_PK1_2D(F): + U, sig, V = ti.svd(F) + inv_sig = sig.inverse() + e = ti.Matrix([[ti.log(sig[0, 0]), 0], [0, ti.log(sig[1, 1])]]) + return U @ (2 * mu * inv_sig @ e + lam * e.trace() * inv_sig) @ V.transpose() +# ANCHOR_END: stvk + +################################ +# Drucker Prager plasticity +################################ +# ANCHOR: drucker_prager +@ti.func +def Drucker_Prager_return_mapping(F, diff_log_J): + dim = ti.static(F.n) + sin_phi = ti.sin(friction_angle_in_degrees/ 180.0 * ti.math.pi) + friction_alpha = ti.sqrt(2.0 / 3.0) * 2.0 * sin_phi / (3.0 - sin_phi) + U, sig_diag, V = ti.svd(F) + sig = ti.Vector([ti.max(sig_diag[i,i], 0.05) for i in ti.static(range(dim))]) + epsilon = ti.log(sig) + epsilon += diff_log_J / dim # volume correction treatment + trace_epsilon = epsilon.sum() + shifted_trace = trace_epsilon + if shifted_trace >= 0: + for d in ti.static(range(dim)): + epsilon[d] = 0. + else: + epsilon_hat = epsilon - (trace_epsilon / dim) + epsilon_hat_norm = ti.sqrt(epsilon_hat.dot(epsilon_hat)+1e-8) + delta_gamma = epsilon_hat_norm + (dim * lam + 2. * mu) / (2. * mu) * (shifted_trace) * friction_alpha + epsilon -= (ti.max(delta_gamma, 0) / epsilon_hat_norm) * epsilon_hat + sig_out = ti.exp(epsilon) + for d in ti.static(range(dim)): + sig_diag[d,d] = sig_out[d] + return U @ sig_diag @ V.transpose() +# ANCHOR_END: drucker_prager + +# Particle-to-Grid (P2G) Transfers +# ANCHOR: p2g +@ti.kernel +def particle_to_grid_transfer(): + for p in range(N_particles): + base = (x[p] / dx - 0.5).cast(int) + fx = x[p] / dx - base.cast(float) + # quadratic B-spline interpolating functions + w = [0.5 * (1.5 - fx) ** 2, 0.75 - (fx - 1) ** 2, 0.5 * (fx - 0.5) ** 2] + # gradient of the interpolating function + dw_dx = [fx - 1.5, 2 * (1.0 - fx), fx - 0.5] + + P = StVK_Hencky_PK1_2D(F[p]) + for i in ti.static(range(3)): + for j in ti.static(range(3)): + offset = ti.Vector([i, j]) + dpos = (offset.cast(float) - fx) * dx + weight = w[i][0] * w[j][1] + grad_weight = ti.Vector([(1. / dx) * dw_dx[i][0] * w[j][1], + w[i][0] * (1. / dx) * dw_dx[j][1]]) + + grid_m[base + offset] += weight * m[p] # mass transfer + # ANCHOR: apic_p2g + grid_v[base + offset] += weight * m[p] * (v[p] + C[p] @ dpos) # momentum Transfer, APIC formulation + # ANCHOR_END: apic_p2g + # internal force (stress) transfer + fi = -vol[p] * P @ F[p].transpose() @ grad_weight + grid_v[base + offset] += dt * fi +# ANCHOR_END: p2g + +# Grid Update +@ti.kernel +def update_grid(): + for i, j in grid_m: + if grid_m[i, j] > 0: + grid_v[i, j] = grid_v[i, j] / grid_m[i, j] # extract updated nodal velocity from transferred nodal momentum + grid_v[i, j] += ti.Vector([0, -9.81]) * dt # gravity + + # Dirichlet BC near the bounding box + if i <= 3 or i > grid_size - 3 or j <= 2 or j > grid_size - 3: + grid_v[i, j] = 0 + + x_i = (ti.Vector([i, j])) * dx # position of the grid-node + + # ANCHOR: sphere_sdf + # a sphere SDF as boundary condition + sphere_center = ti.Vector([0.5, 0.5]) + sphere_radius = 0.05 + dx # add a dx-gap to avoid penetration + if (x_i - sphere_center).norm() < sphere_radius: + normal = (x_i - sphere_center).normalized() + diff_vel = -grid_v[i, j] + dotnv = normal.dot(diff_vel) + dotnv_frac = dotnv * (1.0 - sdf_friction) + grid_v[i, j] += diff_vel * sdf_friction + normal * dotnv_frac + # ANCHOR_END: sphere_sdf + + +# Grid-to-Particle (G2P) Transfers +# ANCHOR: g2p +@ti.kernel +def grid_to_particle_transfer(): + for p in range(N_particles): + base = (x[p] / dx - 0.5).cast(int) + fx = x[p] / dx - base.cast(float) + # quadratic B-spline interpolating functions + w = [0.5 * (1.5 - fx) ** 2, 0.75 - (fx - 1) ** 2, 0.5 * (fx - 0.5) ** 2] + # gradient of the interpolating function + dw_dx = [fx - 1.5, 2 * (1.0 - fx), fx - 0.5] + + new_v = ti.Vector.zero(float, 2) + new_C = ti.Matrix.zero(float, 2, 2) + v_grad_wT = ti.Matrix.zero(float, 2, 2) + for i in ti.static(range(3)): + for j in ti.static(range(3)): + offset = ti.Vector([i, j]) + dpos = (offset.cast(float) - fx) * dx + weight = w[i][0] * w[j][1] + grad_weight = ti.Vector([(1. / dx) * dw_dx[i][0] * w[j][1], + w[i][0] * (1. / dx) * dw_dx[j][1]]) + + new_v += weight * grid_v[base + offset] + # ANCHOR: apic_g2p + new_C += weight * grid_v[base + offset].outer_product(dpos) / D + # ANCHOR_END: apic_g2p + v_grad_wT += grid_v[base + offset].outer_product(grad_weight) + + v[p] = new_v + C[p] = new_C + # note the updated F here is the trial elastic deformation gradient + F[p] = (ti.Matrix.identity(float, 2) + dt * v_grad_wT) @ F[p] +# ANCHOR_END: g2p + +# Deformation Gradient and Particle State Update +# ANCHOR: particle_update +@ti.kernel +def update_particle_state(): + for p in range(N_particles): + # trial elastic deformation gradient + F_tr = F[p] + # apply return mapping to correct the trial elastic state, projecting the stress induced by F_tr + # back onto the yield surface, following the direction specified by the plastic flow rule. + new_F = Drucker_Prager_return_mapping(F_tr, diff_log_J[p]) + # track the volume change incurred by return mapping to correct volume, following https://dl.acm.org/doi/10.1145/3072959.3073651 sec 4.3.4 + diff_log_J[p] += -ti.log(new_F.determinant()) + ti.log(F_tr.determinant()) + F[p] = new_F + # advection + x[p] += dt * v[p] +# ANCHOR_END: particle_update + +# ANCHOR: time_step +def step(): + # a single time step of the Material Point Method (MPM) simulation + reset_grid() + particle_to_grid_transfer() + update_grid() + grid_to_particle_transfer() + update_particle_state() +# ANCHOR_END: time_step + +################################ +# Main +################################ +gui = ti.GUI("2D MPM Sand", res = 512, background_color = 0xFFFFFF) +frame = 0 +while True: + for s in range(50): + step() + + gui.circles(np.array([[0.5, 0.5]]), radius = 0.05 * gui.res[0], color = 0xFF0000) + gui.circles(x.to_numpy(), radius = 1.5, color = 0xD6B588) + gui.show() \ No newline at end of file diff --git a/11_mpm_plastic/simulator_viscoplastic.py b/11_mpm_plastic/simulator_viscoplastic.py new file mode 100644 index 0000000..8a65b6d --- /dev/null +++ b/11_mpm_plastic/simulator_viscoplastic.py @@ -0,0 +1,276 @@ +import taichi as ti +import os +import shutil + +ti.init(arch=ti.cuda) + +quality = 6 +n_particles, n_grid = 9000 * quality**2, 256 * quality +dx, inv_dx = 1 / n_grid, float(n_grid) +dt = 1e-4 / quality +p_vol, p_rho = (dx * 0.5) ** 2, 1 +p_mass = p_vol * p_rho + +nu = 0.2 +E_toothpaste = 350.0 +mu_toothpaste = E_toothpaste / (2 * (1 + nu)) +lam_toothpaste = E_toothpaste * nu / ((1 + nu) * (1 - 2 * nu)) + +yield_stress_bar1 = 1.2 +plastic_viscosity_bar1 = 0.7 +yield_stress_bar2 = 1.0 +plastic_viscosity_bar2 = 0.3 + +ground_friction = 0.3 + +x = ti.Vector.field(2, dtype=float, shape=n_particles) +v = ti.Vector.field(2, dtype=float, shape=n_particles) +C = ti.Matrix.field(2, 2, dtype=float, shape=n_particles) +F = ti.Matrix.field(2, 2, dtype=float, shape=n_particles) +color_stripe = ti.field(dtype=int, shape=n_particles) +yield_stress = ti.field(dtype=float, shape=n_particles) +plastic_viscosity = ti.field(dtype=float, shape=n_particles) +grid_v = ti.Vector.field(2, dtype=float, shape=(n_grid, n_grid)) +grid_m = ti.field(dtype=float, shape=(n_grid, n_grid)) +gravity = ti.Vector.field(2, dtype=float, shape=()) + + +@ti.func +def viscoplastic_return_mapping_stvk_2d(F_trial, mu_p, lam_p, yield_stress_p, plastic_viscosity_p, dt_val): + """Viscoplastic return mapping for toothpaste-like material (2D version)""" + U, sig, V = ti.svd(F_trial) + + # Clamp singular values to prevent numerical issues + sig0 = ti.max(sig[0, 0], 0.01) + sig1 = ti.max(sig[1, 1], 0.01) + + # Compute logarithmic strain (2D) + epsilon = ti.Vector([ti.log(sig0), ti.log(sig1)]) + trace_epsilon = epsilon[0] + epsilon[1] + + # Deviatoric strain + epsilon_hat = epsilon - ti.Vector([trace_epsilon / 2.0, trace_epsilon / 2.0]) + + # Deviatoric stress in logarithmic strain space + s_trial = 2.0 * mu_p * epsilon_hat + s_trial_norm = s_trial.norm() + + # Yield condition - using similar factor to 3D version (sqrt(2/3) ≈ 0.816) + # For 2D, we use sqrt(2/3) to match the 3D implementation's scaling + y = s_trial_norm - ti.sqrt(2.0 / 3.0) * yield_stress_p + + F_elastic_res = F_trial + if y > 0: + # Compute b_trial for mu_hat (2D adaptation) + b_trial = sig0 * sig0 + sig1 * sig1 + mu_hat = mu_p * b_trial / 2.0 + + # Rate-dependent plastic flow + denom = 1.0 + plastic_viscosity_p / (2.0 * mu_hat * dt_val) + s_new_norm = s_trial_norm - y / denom + s_scale = s_new_norm / s_trial_norm if s_trial_norm > 1e-10 else 1.0 + s_new = s_scale * s_trial + + # Reconstruct strain + epsilon_new = 1.0 / (2.0 * mu_p) * s_new + ti.Vector([trace_epsilon / 2.0, trace_epsilon / 2.0]) + + # Reconstruct deformation gradient + sig_elastic = ti.Matrix([[ti.exp(epsilon_new[0]), 0.0], [0.0, ti.exp(epsilon_new[1])]]) + F_elastic_res = U @ sig_elastic @ V.transpose() + + return F_elastic_res + + +@ti.func +def stvk_stress_2d(F_elastic, U, V, sig, mu_p, lam_p): + """Saint Venant-Kirchhoff stress model (2D version)""" + sig0 = ti.max(sig[0, 0], 0.01) + sig1 = ti.max(sig[1, 1], 0.01) + + epsilon = ti.Vector([ti.log(sig0), ti.log(sig1)]) + log_sig_sum = ti.log(sig0) + ti.log(sig1) + + ONE = ti.Vector([1.0, 1.0]) + tau = 2.0 * mu_p * epsilon + lam_p * log_sig_sum * ONE + + tau_mat = ti.Matrix([[tau[0], 0.0], [0.0, tau[1]]]) + return U @ tau_mat @ V.transpose() @ F_elastic.transpose() + + +@ti.kernel +def p2g2p(): + for i, j in grid_m: + grid_v[i, j] = [0, 0] + grid_m[i, j] = 0 + for p in x: + if x[p][0] < 0.0 or x[p][1] < 0.0 or x[p][0] > 1.0 or x[p][1] > 1.0: + continue + + base = (x[p] * inv_dx - 0.5).cast(int) + fx = x[p] * inv_dx - base.cast(float) + w = [0.5 * (1.5 - fx) ** 2, 0.75 - (fx - 1) ** 2, 0.5 * (fx - 0.5) ** 2] + F_trial = (ti.Matrix.identity(float, 2) + dt * C[p]) @ F[p] + + F[p] = viscoplastic_return_mapping_stvk_2d( + F_trial, mu_toothpaste, lam_toothpaste, yield_stress[p], plastic_viscosity[p], dt + ) + + U, sig, V = ti.svd(F[p]) + stress = stvk_stress_2d(F[p], U, V, sig, mu_toothpaste, lam_toothpaste) + + stress = (-dt * p_vol * 4 * inv_dx * inv_dx) * stress + affine = stress + p_mass * C[p] + for i, j in ti.static(ti.ndrange(3, 3)): + offset = ti.Vector([i, j]) + dpos = (offset.cast(float) - fx) * dx + weight = w[i][0] * w[j][1] + grid_v[base + offset] += weight * (p_mass * v[p] + affine @ dpos) + grid_m[base + offset] += weight * p_mass + for i, j in grid_m: + if grid_m[i, j] > 0: + grid_v[i, j] = (1 / grid_m[i, j]) * grid_v[i, j] + grid_v[i, j] += dt * gravity[None] * 30 + + if i < 3 and grid_v[i, j][0] < 0: + grid_v[i, j][0] = 0 + if i > n_grid - 3 and grid_v[i, j][0] > 0: + grid_v[i, j][0] = 0 + + if j < 3 and grid_v[i, j][1] < 0: + v_y = grid_v[i, j][1] + v_x = grid_v[i, j][0] + normal_component = ti.abs(v_y) + tangential_velocity = v_x + + if ti.abs(tangential_velocity) > 1e-20: + friction_reduction = ground_friction * normal_component + v_x_new = tangential_velocity + if v_x_new > 0: + v_x_new = ti.max(0.0, v_x_new - friction_reduction) + else: + v_x_new = ti.min(0.0, v_x_new + friction_reduction) + grid_v[i, j] = ti.Vector([v_x_new, 0.0]) + else: + grid_v[i, j] = ti.Vector([0.0, 0.0]) + + if j > n_grid - 3 and grid_v[i, j][1] > 0: + grid_v[i, j][1] = 0 + for p in x: + if x[p][0] < 0.0 or x[p][1] < 0.0 or x[p][0] > 1.0 or x[p][1] > 1.0: + continue + + base = (x[p] * inv_dx - 0.5).cast(int) + fx = x[p] * inv_dx - base.cast(float) + w = [0.5 * (1.5 - fx) ** 2, 0.75 - (fx - 1.0) ** 2, 0.5 * (fx - 0.5) ** 2] + new_v = ti.Vector.zero(float, 2) + new_C = ti.Matrix.zero(float, 2, 2) + for i, j in ti.static(ti.ndrange(3, 3)): + dpos = ti.Vector([i, j]).cast(float) - fx + g_v = grid_v[base + ti.Vector([i, j])] + weight = w[i][0] * w[j][1] + new_v += weight * g_v + new_C += 4 * inv_dx * weight * g_v.outer_product(dpos) + v[p], C[p] = new_v, new_C + x[p] += dt * v[p] + + +@ti.kernel +def reset(): + bar_width = 0.015 + bar_height = 0.85 + bar_bottom_y = 0.1 + bar_spacing = 0.2 + bar1_center_x = 0.5 - bar_spacing / 2.0 + bar2_center_x = 0.5 + bar_spacing / 2.0 + + particles_per_bar = n_particles // 2 + + for i in range(n_particles): + bar_center_x = 0.5 + bar_yield_stress = 1.2 + bar_plastic_viscosity = 0.7 + + if i < particles_per_bar: + bar_center_x = bar1_center_x + bar_yield_stress = 1.2 + bar_plastic_viscosity = 0.7 + else: + bar_center_x = bar2_center_x + bar_yield_stress = 1.0 + bar_plastic_viscosity = 0.3 + + x_pos = ti.random() * bar_width + (bar_center_x - bar_width / 2.0) + y_pos = ti.random() * bar_height + bar_bottom_y + + x[i] = [x_pos, y_pos] + + stripe_width = bar_width / 3.0 + relative_x = x_pos - (bar_center_x - bar_width / 2.0) + if relative_x < stripe_width: + color_stripe[i] = 0 + elif relative_x < 2.0 * stripe_width: + color_stripe[i] = 1 + else: + color_stripe[i] = 2 + + v[i] = [0, 0] + F[i] = ti.Matrix([[1, 0], [0, 1]]) + C[i] = ti.Matrix.zero(float, 2, 2) + yield_stress[i] = bar_yield_stress + plastic_viscosity[i] = bar_plastic_viscosity + + +gui = ti.GUI("Taichi MLS-MPM-128", res=1024, background_color=0xEEEEF0, show_gui=False) +reset() +gravity[None] = [0, -1] + +save_duration = 10.0 +output_fps = 30 +frame_time = 3e-2 +total_frames_to_run = int(save_duration / frame_time) +frames_per_save = int(1.0 / (output_fps * frame_time)) +total_saves = int(save_duration * output_fps) +save_counter = 0 + +output_dir = os.path.join(os.path.dirname(__file__), "frames") +os.makedirs(output_dir, exist_ok=True) +video_output = os.path.join(os.path.dirname(__file__), "viscoplastic_animation.mp4") + + +for frame in range(total_frames_to_run): + substeps_per_frame = int(2e-3 // dt) + + for s in range(substeps_per_frame): + p2g2p() + + if frame % frames_per_save == 0 and save_counter < total_saves: + gui.circles( + x.to_numpy(), + radius=1.5, + palette=[0x3366FF, 0xFFFF00, 0xFF3333], + palette_indices=color_stripe, + ) + filename = os.path.join(output_dir, f'{save_counter:06d}.png') + gui.show(filename) + save_counter += 1 + if save_counter % 30 == 0: + print(f"Saved {save_counter}/{total_saves} frames...") + +print(f"Frame saving complete! Saved {save_counter} frames.") + +ffmpeg_path = shutil.which("ffmpeg") +if ffmpeg_path is not None and save_counter > 0: + pattern = os.path.join(output_dir, "%06d.png") + cmd = ( + f'"{ffmpeg_path}" -y -framerate {output_fps} -i "{pattern}" ' + f'-c:v libx264 -pix_fmt yuv420p -crf 18 "{video_output}"' + ) + print("Running:", cmd) + os.system(cmd) + print(f"Video written to: {video_output}") +else: + print("ffmpeg not found or no frames saved. To build video manually, run:") + print( + f"ffmpeg -y -framerate {output_fps} -i '{os.path.join(output_dir, '%06d.png')}' " + f"-c:v libx264 -pix_fmt yuv420p -crf 18 '{video_output}'" + ) \ No newline at end of file diff --git a/12_pbd_cloth/cloth_data.json b/12_pbd_cloth/cloth_data.json new file mode 100644 index 0000000..3cbfd70 --- /dev/null +++ b/12_pbd_cloth/cloth_data.json @@ -0,0 +1,1952 @@ + { + "name" : "cloth", + "vertices" : [ + -0.200000, 1.145859, -0.000000, -0.200000, 1.105859, -0.000000, -0.200000, 1.065859, -0.000000, -0.200000, 1.025859, -0.000000, -0.200000, 0.985859, -0.000000, + -0.200000, 0.945859, -0.000000, -0.200000, 0.905859, -0.000000, -0.200000, 0.865859, -0.000000, -0.200000, 0.825859, -0.000000, -0.200000, 0.785859, -0.000000, + -0.200000, 0.745859, -0.000000, -0.200000, 0.705859, -0.000000, -0.200000, 0.665859, -0.000000, -0.200000, 0.625859, -0.000000, -0.200000, 0.585859, -0.000000, + -0.200000, 0.545859, -0.000000, -0.200000, 0.505859, -0.000000, 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b/12_pbd_cloth/simulator.py @@ -0,0 +1,415 @@ +import taichi as ti +import numpy as np +import json +import math +import time +import warp as wp +import warp.render + +ti.init(arch=ti.cpu, default_fp=ti.f64) + +class USDExporter: + def __init__(self, output_path="cloth_animation.usd", fps=60, scale=10.0): + self.output_path = output_path + self.fps = fps + self.scale = scale + self.frame_dt = 1.0 / fps + self.sim_time = 0.0 + self.frame_count = 0 + + self.renderer = wp.render.UsdRenderer(output_path, scaling=scale) + self.renderer.render_ground() + + print(f"USD exporter initialized: {output_path}") + print(f"FPS: {fps}") + print(f"Scale: {scale}x") + + def export_frame(self, positions, indices): + self.renderer.begin_frame(self.sim_time) + + self.renderer.render_mesh( + name="cloth_mesh", + points=positions, + indices=indices + ) + + self.renderer.end_frame() + + self.frame_count += 1 + self.sim_time += self.frame_dt + + if self.frame_count % 60 == 0: + print(f"Exported frame {self.frame_count} at time {self.sim_time:.3f}s") + + def save(self): + self.renderer.save() + print(f"\nUSD animation saved: {self.output_path}") + print(f"Total frames: {self.frame_count}") + print(f"Duration: {self.sim_time:.3f} seconds") + print(f"\nTo import into Blender:") + print(f"1. File > Import > Universal Scene Description (.usd)") + print(f"2. Select '{self.output_path}'") + print(f"3. The animation will be imported as a single animated sequence!") + +def load_cloth_data_from_json(filepath="cloth_data.json"): + try: + with open(filepath, 'r') as f: + data = json.load(f) + vertices = np.array(data['vertices'], dtype=np.float64).reshape((-1, 3)) + face_tri_ids = np.array(data['faceTriIds'], dtype=np.int32) + print(f"Loaded cloth data: {len(vertices)} vertices, {len(face_tri_ids)//3} triangles") + return vertices, face_tri_ids + except Exception as e: + print(f"Error loading cloth data from {filepath}: {e}") + print("Falling back to procedural cloth generation...") + verts_np, tris_np = create_cloth_mesh_data() + return verts_np, tris_np.flatten() + +def create_cloth_mesh_data(width=20, height=15, spacing=0.1): + num_particles = width * height + verts = np.zeros((num_particles, 3), dtype=np.float64) + offset_x = - (width - 1) * spacing / 2.0 + offset_y = - (height - 1) * spacing / 2.0 + (height * spacing * 0.8) + for y in range(height): + for x in range(width): + idx = y * width + x + verts[idx] = [x * spacing + offset_x, y * spacing + offset_y, 0] + num_tris = 2 * (width - 1) * (height - 1) + tri_ids = np.zeros((num_tris, 3), dtype=np.int32) + tri_idx = 0 + for y in range(height - 1): + for x in range(width - 1): + p0, p1, p2, p3 = y*width+x, y*width+x+1, (y+1)*width+x, (y+1)*width+x+1 + tri_ids[tri_idx], tri_idx = [p0, p1, p2], tri_idx + 1 + tri_ids[tri_idx], tri_idx = [p1, p3, p2], tri_idx + 1 + return verts, tri_ids + +def find_constraint_indices(tri_ids_np): + edge_to_tri_map = {} + for i, tri in enumerate(tri_ids_np): + for j in range(3): + v0_idx, v1_idx = tri[j], tri[(j + 1) % 3] + edge = tuple(sorted((v0_idx, v1_idx))) + if edge not in edge_to_tri_map: + edge_to_tri_map[edge] = [] + edge_to_tri_map[edge].append(i) + stretching_ids = list(edge_to_tri_map.keys()) + bending_ids = [] + for edge, tris in edge_to_tri_map.items(): + if len(tris) == 2: + tri0_idx, tri1_idx = tris[0], tris[1] + p2 = [v for v in tri_ids_np[tri0_idx] if v not in edge][0] + p3 = [v for v in tri_ids_np[tri1_idx] if v not in edge][0] + bending_ids.append([p2, p3]) + return np.array(stretching_ids, dtype=np.int32), np.array(bending_ids, dtype=np.int32) + +paused = True +gravity = ti.Vector([0.0, -9.8, 0.0]) +dt = 1.0 / 60.0 +num_substeps = 15 +sdt = dt / num_substeps +solver_iterations = 1 + +export_enabled = False +export_frame_count = 0 +usd_exporter = None + +verts_np, face_tri_ids_np = load_cloth_data_from_json() +tris_np = face_tri_ids_np.reshape((-1, 3)) +stretching_ids_np, bending_ids_np = find_constraint_indices(tris_np) + +num_particles = len(verts_np) +num_tris = len(tris_np) +num_stretching_constraints = len(stretching_ids_np) +num_bending_constraints = len(bending_ids_np) + +stretching_compliance = 0.0 +bending_compliance = 1.0 + +pos = ti.Vector.field(3, dtype=ti.f64, shape=num_particles) +prev_pos = ti.Vector.field(3, dtype=ti.f64, shape=num_particles) +vel = ti.Vector.field(3, dtype=ti.f64, shape=num_particles) +inv_mass = ti.field(dtype=ti.f64, shape=num_particles) +original_inv_mass = ti.field(dtype=ti.f64, shape=num_particles) + +tri_ids = ti.field(ti.i32, shape=num_tris * 3) +stretching_ids = ti.field(ti.i32, shape=(num_stretching_constraints, 2)) +bending_ids = ti.field(ti.i32, shape=(num_bending_constraints, 2)) + +stretching_lengths = ti.field(dtype=ti.f64, shape=num_stretching_constraints) +bending_lengths = ti.field(dtype=ti.f64, shape=num_bending_constraints) + +ground_vertices = ti.Vector.field(3, dtype=ti.f64, shape=4) +ground_indices = ti.field(ti.i32, shape=6) +grab_indicator_pos = ti.Vector.field(3, dtype=ti.f64, shape=1) + +vertex_colors = ti.Vector.field(3, dtype=ti.f64, shape=num_particles) + +pos.from_numpy(verts_np) +tri_ids.from_numpy(tris_np.flatten()) +stretching_ids.from_numpy(stretching_ids_np) +bending_ids.from_numpy(bending_ids_np) +ground_vertices.from_numpy(np.array([[-10, 0, -10], [10, 0, -10], [10, 0, 10], [-10, 0, 10]], dtype=np.float64)) +ground_indices.from_numpy(np.array([0, 1, 2, 0, 2, 3], dtype=np.int32)) + +@ti.kernel +def init_physics(): + for i in range(num_particles): + prev_pos[i] = pos[i] + vel[i] = ti.Vector([0.0, 0.0, 0.0]) + inv_mass.fill(0.0) + for i in range(num_tris): + id0, id1, id2 = tri_ids[i * 3], tri_ids[i * 3 + 1], tri_ids[i * 3 + 2] + p0, p1, p2 = pos[id0], pos[id1], pos[id2] + area = 0.5 * (p1 - p0).cross(p2 - p0).norm() + p_inv_mass = 1.0 / (area / 3.0) if area > 0 else 0.0 + inv_mass[id0] += p_inv_mass + inv_mass[id1] += p_inv_mass + inv_mass[id2] += p_inv_mass + for i in range(num_stretching_constraints): + id0, id1 = stretching_ids[i, 0], stretching_ids[i, 1] + stretching_lengths[i] = (pos[id0] - pos[id1]).norm() + for i in range(num_bending_constraints): + id0, id1 = bending_ids[i, 0], bending_ids[i, 1] + bending_lengths[i] = (pos[id0] - pos[id1]).norm() + for i in range(num_particles): + original_inv_mass[i] = inv_mass[i] + +@ti.kernel +def pin_top_vertices(): + max_y = -1e9 + for i in range(num_particles): + if pos[i].y > max_y: + max_y = pos[i].y + for i in range(num_particles): + if pos[i].y >= max_y - 1e-6: + inv_mass[i] = 0.0 + +@ti.kernel +def initialize_colors(): + for i in range(num_particles): + x_coord = int((pos[i].x + 1.0) * 5) % 2 + z_coord = int((pos[i].z + 1.0) * 5) % 2 + + if (x_coord + z_coord) % 2 == 0: + vertex_colors[i] = ti.Vector([1.0, 1.0, 1.0]) + else: + vertex_colors[i] = ti.Vector([0.1, 0.1, 0.1]) + +@ti.kernel +def apply_grab(particle_idx: ti.i32, target_x: ti.f64, target_y: ti.f64, target_z: ti.f64): + if particle_idx != -1: + target_pos = ti.Vector([target_x, target_y, target_z]) + pos[particle_idx] = target_pos + vel[particle_idx] = ti.Vector([0.0, 0.0, 0.0]) + grab_indicator_pos[0] = target_pos + +@ti.kernel +def pre_solve(dt: ti.f64): + for i in range(num_particles): + if inv_mass[i] == 0.0: continue + vel[i] += gravity * dt + prev_pos[i] = pos[i] + pos[i] += vel[i] * dt + if pos[i].y < 0.0: + pos[i] = prev_pos[i] + pos[i].y = 0.0 + +@ti.kernel +def solve_stretching_constraints(compliance: ti.f64, dt: ti.f64): + alpha = compliance / (dt * dt) + for i in range(num_stretching_constraints): + id0, id1 = stretching_ids[i, 0], stretching_ids[i, 1] + w0, w1 = inv_mass[id0], inv_mass[id1] + w_sum = w0 + w1 + if w_sum == 0.0: continue + p0, p1 = pos[id0], pos[id1] + delta = p0 - p1 + dist = delta.norm() + if dist == 0.0: continue + grad = delta / dist + C = dist - stretching_lengths[i] + s = -C / (w_sum + alpha) + pos[id0] += s * w0 * grad + pos[id1] -= s * w1 * grad + +@ti.kernel +def solve_bending_constraints(compliance: ti.f64, dt: ti.f64): + alpha = compliance / (dt * dt) + for i in range(num_bending_constraints): + id0, id1 = bending_ids[i, 0], bending_ids[i, 1] + w0, w1 = inv_mass[id0], inv_mass[id1] + w_sum = w0 + w1 + if w_sum == 0.0: continue + p0, p1 = pos[id0], pos[id1] + delta = p0 - p1 + dist = delta.norm() + if dist == 0.0: continue + grad = delta / dist + C = dist - bending_lengths[i] + s = -C / (w_sum + alpha) + pos[id0] += s * w0 * grad + pos[id1] -= s * w1 * grad + +@ti.kernel +def post_solve(dt: ti.f64): + for i in range(num_particles): + if inv_mass[i] == 0.0: continue + vel[i] = (pos[i] - prev_pos[i]) / dt + +def substep(grab_id, grab_x, grab_y, grab_z): + pre_solve(sdt) + for _ in range(solver_iterations): + solve_stretching_constraints(stretching_compliance, sdt) + solve_bending_constraints(bending_compliance, sdt) + apply_grab(grab_id, grab_x, grab_y, grab_z) + post_solve(sdt) + +def find_bottom_corner(): + positions = pos.to_numpy() + min_y = float('inf') + min_x = float('inf') + corner_idx = -1 + + for i in range(num_particles): + if positions[i, 1] < min_y: + min_y = positions[i, 1] + + for i in range(num_particles): + if abs(positions[i, 1] - min_y) < 1e-6: + if positions[i, 0] < min_x: + min_x = positions[i, 0] + corner_idx = i + + print(f"Found bottom corner particle: {corner_idx} at position ({min_x:.3f}, {min_y:.3f})") + return corner_idx + +def calculate_quadratic_path_pos(start_pos, end_pos, t): + t_squared = t * t + scaled_displacement = (end_pos - start_pos) * 0.3 + return start_pos + scaled_displacement * t_squared + +init_physics() +pin_top_vertices() +initialize_colors() + +window = ti.ui.Window("Taichi XPBD Cloth", (1024, 1024), vsync=True) +canvas = window.get_canvas() +scene = window.get_scene() +camera = ti.ui.Camera() +camera.position(0, 1.0, 3.0) +camera.lookat(0, 0.5, 0) + +is_grabbing = False +grabbed_particle_id = -1 +grab_distance = 0.0 +bottom_corner_id = find_bottom_corner() + +is_animating = False +animation_start_time = 0.0 +animation_duration = 2.0 +original_corner_pos = None +target_corner_pos = None +start_time = time.time() + +while window.running: + gui = window.GUI + with gui.sub_window("Controls", 0.05, 0.05, 0.3, 0.4): + paused = gui.checkbox("Paused", paused) + bending_compliance = gui.slider_float("Bending Compliance", bending_compliance, 0.0, 10.0) + + gui.text("Bottom Corner Control:") + if gui.button("Animate Corner"): + if not is_animating and not is_grabbing: + is_animating = True + is_grabbing = True + grabbed_particle_id = bottom_corner_id + inv_mass[grabbed_particle_id] = 0.0 + + original_corner_pos = pos[grabbed_particle_id] + target_corner_pos = ti.Vector([original_corner_pos.x - 0.3, original_corner_pos.y + 0.5, original_corner_pos.z + 0.2]) + animation_start_time = 0.0 + + if gui.button("Release Corner"): + if is_grabbing and grabbed_particle_id != -1: + inv_mass[grabbed_particle_id] = original_inv_mass[grabbed_particle_id] + is_grabbing = False + is_animating = False + grabbed_particle_id = -1 + + if is_animating: + current_time = time.time() + elapsed_time = current_time - animation_start_time + progress = min(1.0, elapsed_time / animation_duration) + gui.text(f"Animation Progress: {progress:.1%}") + + gui.text("Export:") + export_enabled = gui.checkbox("Export Animation", export_enabled) + + if export_enabled and usd_exporter is None: + usd_exporter = USDExporter("cloth_animation.usd", fps=60, scale=10.0) + print("USD exporter initialized!") + + gui.text(f"Exported Frames: {export_frame_count}") + if usd_exporter: + gui.text(f"USD File: {usd_exporter.output_path}") + + if gui.button("Reset"): + pos.from_numpy(verts_np) + init_physics() + pin_top_vertices() + is_grabbing = False + is_animating = False + grabbed_particle_id = -1 + + grab_target_position = ti.Vector([0.0, 0.0, 0.0]) + + if is_animating and grabbed_particle_id != -1: + if animation_start_time == 0.0: + animation_start_time = time.time() + + current_time = time.time() + elapsed_time = current_time - animation_start_time + + if elapsed_time < animation_duration: + t = elapsed_time / animation_duration + t = max(0.0, min(1.0, t)) + + grab_target_position = calculate_quadratic_path_pos(original_corner_pos, target_corner_pos, t) + else: + grab_target_position = target_corner_pos + is_animating = False + + elif is_grabbing and grabbed_particle_id != -1: + grab_target_position = pos[grabbed_particle_id] + + if not paused: + for _ in range(num_substeps): + substep(grabbed_particle_id, grab_target_position.x, grab_target_position.y, grab_target_position.z) + + if export_enabled and usd_exporter: + particle_positions = pos.to_numpy() + triangle_indices = tri_ids.to_numpy() + + usd_exporter.export_frame(particle_positions, triangle_indices) + export_frame_count += 1 + + camera.track_user_inputs(window, movement_speed=0.03, hold_key=ti.ui.RMB) + scene.set_camera(camera) + scene.ambient_light((0.5, 0.5, 0.5)) + scene.point_light(pos=(2, 3, 4), color=(1, 1, 1)) + + scene.mesh(pos, indices=tri_ids, per_vertex_color=vertex_colors, two_sided=True) + scene.mesh(ground_vertices, indices=ground_indices, color=(0.8, 0.8, 0.8)) + + if is_grabbing: + scene.particles(grab_indicator_pos, radius=0.01, color=(1.0, 1.0, 0.0)) + + canvas.scene(scene) + window.show() + +if usd_exporter and export_frame_count > 0: + usd_exporter.save() + print(f"\nAnimation export complete!") + print(f"Total frames exported: {export_frame_count}") + print(f"USD file: {usd_exporter.output_path}") diff --git a/13_pbd_mesh/dragon_data.json b/13_pbd_mesh/dragon_data.json new file mode 100644 index 0000000..55d8304 --- /dev/null +++ b/13_pbd_mesh/dragon_data.json @@ -0,0 +1,29049 @@ + +{ + "verts" : [ +-0.067935, 1.288305, -0.082477, 0.003506, 1.248151, -0.070033, 0.001571, 1.244475, -0.167807, -0.082122, 1.289001, -0.158913, +0.075577, 1.205556, -0.085262, 0.086003, 1.196606, -0.169586, -0.000598, 1.241600, -0.265073, -0.075249, 1.280443, -0.233302, +0.072027, 1.200585, -0.252378, -0.181908, 1.304366, -0.112030, -0.133853, 1.321139, -0.019623, 0.128278, 1.171134, -0.319993, +-0.008263, 1.234653, -0.372647, 0.002688, 1.257620, 0.033030, -0.174918, 1.282726, -0.218455, 0.136393, 1.188153, -0.019390, +0.179567, 1.156401, -0.169651, 0.103378, 1.359907, -0.076255, 0.054315, 1.421892, -0.080737, 0.104871, 1.371044, -0.172360, +0.038392, 1.432074, -0.161453, 0.153649, 1.296934, 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except Exception as e: + print(f"Error loading or parsing {filepath}: {e}") + exit() + + sim_verts_np = np.array(data['verts'], dtype=np.float64).reshape((-1, 3)) + tet_ids_np = np.array(data['tetIds'], dtype=np.int32).reshape((-1, 4)) + edge_ids_np = np.array(data['edgeIds'], dtype=np.int32).reshape((-1, 2)) + + vis_data = data.get('dragonVis') + if not vis_data: + print("Error: JSON file must contain a 'dragonVis' object for the visual mesh.") + exit() + vis_verts_np = np.array(vis_data['verts'], dtype=np.float64).reshape((-1, 3)) + vis_tri_ids_np = np.array(vis_data['triIds'], dtype=np.int32) + + return { + "sim_verts": sim_verts_np, "tet_ids": tet_ids_np, "edge_ids": edge_ids_np, + "vis_verts": vis_verts_np, "vis_tri_ids": vis_tri_ids_np + } + +class USDExporter: + + def __init__(self, output_path="dragon_animation.usd", fps=60, scale=1.0): + self.output_path = output_path + self.fps = fps + self.scale = scale + self.frame_dt = 1.0 / fps + self.sim_time = 0.0 + self.frame_count = 0 + + # Initialize Warp USD renderer with scaling + self.renderer = wp.render.UsdRenderer(output_path, scaling=scale) + self.renderer.render_ground() + + print(f"USD exporter initialized: {output_path}") + print(f"FPS: {fps}") + print(f"Scale: {scale}x") + + def export_frame(self, vertices, faces): + # Begin frame + self.renderer.begin_frame(self.sim_time) + + # Export dragon mesh (simplified, no colors for better Blender compatibility) + self.renderer.render_mesh( + name="dragon_mesh", + points=vertices, + indices=faces.flatten() + ) + + # End frame + self.renderer.end_frame() + + self.frame_count += 1 + self.sim_time += self.frame_dt + + # Print progress every 60 frames + if self.frame_count % 60 == 0: + print(f"Exported frame {self.frame_count} at time {self.sim_time:.3f}s") + + def save(self): + self.renderer.save() + print(f"\nUSD animation saved: {self.output_path}") + print(f"Total frames: {self.frame_count}") + print(f"Duration: {self.sim_time:.3f} seconds") + print(f"\nTo import into Blender:") + print(f"1. File > Import > Universal Scene Description (.usd)") + print(f"2. Select '{self.output_path}'") + print(f"3. The animation will be imported as a single animated sequence!") + +mesh = load_dual_mesh_from_json("dragon_data.json") + +paused = True +gravity = ti.Vector([0.0, -9.8, 0.0]) +dt = 1.0 / 60.0 +num_substeps = 10 +solver_iterations = 5 +sdt = dt / num_substeps + +num_particles = len(mesh["sim_verts"]) +num_tets = len(mesh["tet_ids"]) +num_edges = len(mesh["edge_ids"]) +num_vis_verts = len(mesh["vis_verts"]) +num_vis_tris = len(mesh["vis_tri_ids"]) // 3 + +edge_compliance = 0.0 +vol_compliance = 0.0 +edge_compliance_slider = 0.0 +vol_id_order = [[1, 3, 2], [0, 2, 3], [0, 3, 1], [0, 1, 2]] + +export_enabled = False +export_frame_count = 0 +usd_exporter = None + +CELL_SPACING = 0.05 +inv_cell_spacing = 1.0 / CELL_SPACING +GRID_SIZE = 128 + +pos = ti.Vector.field(3, dtype=ti.f64, shape=num_particles) +prev_pos = ti.Vector.field(3, dtype=ti.f64, shape=num_particles) +vel = ti.Vector.field(3, dtype=ti.f64, shape=num_particles) +inv_mass = ti.field(dtype=ti.f64, shape=num_particles) +rest_vol = ti.field(dtype=ti.f64, shape=num_tets) +edge_lengths = ti.field(dtype=ti.f64, shape=num_edges) +tet_ids = ti.field(ti.i32, shape=(num_tets, 4)) +edge_ids = ti.field(ti.i32, shape=(num_edges, 2)) + +vis_mesh_rest_pos = ti.Vector.field(3, dtype=ti.f64, shape=num_vis_verts) +vis_mesh_pos = ti.Vector.field(3, dtype=ti.f64, shape=num_vis_verts) +vis_mesh_indices = ti.field(ti.i32, shape=num_vis_tris * 3) +vis_mesh_colors = ti.Vector.field(3, dtype=ti.f32, shape=num_vis_verts) + +skinning_info_tet_idx = ti.field(ti.i32, shape=num_vis_verts) +skinning_info_bary_weights = ti.Vector.field(3, dtype=ti.f64, shape=num_vis_verts) +min_dist = ti.field(ti.f64, shape=num_vis_verts) + +grid_cell_counts = ti.field(ti.i32, shape=(GRID_SIZE, GRID_SIZE, GRID_SIZE)) +grid_cell_starts = ti.field(ti.i32, shape=(GRID_SIZE, GRID_SIZE, GRID_SIZE)) +sorted_vis_vert_ids = ti.field(ti.i32, shape=num_vis_verts) + +ground_vertices = ti.Vector.field(3, dtype=ti.f64, shape=4) +ground_indices = ti.field(ti.i32, shape=6) +ground_colors = ti.Vector.field(3, dtype=ti.f32, shape=4) + +BOX_SIZE = 5.0 +box_min = ti.Vector([-BOX_SIZE/2, 0.0, -BOX_SIZE/2]) +box_max = ti.Vector([BOX_SIZE/2, BOX_SIZE, BOX_SIZE/2]) + +pos.from_numpy(mesh["sim_verts"]) +tet_ids.from_numpy(mesh["tet_ids"]) +edge_ids.from_numpy(mesh["edge_ids"]) +vis_mesh_rest_pos.from_numpy(mesh["vis_verts"]) +vis_mesh_indices.from_numpy(mesh["vis_tri_ids"]) +vis_mesh_colors.fill(ti.Vector([0.968, 0.541, 0.113], dt=ti.f32)) +ground_vertices.from_numpy(np.array([[-BOX_SIZE/2,0,-BOX_SIZE/2],[BOX_SIZE/2,0,-BOX_SIZE/2],[BOX_SIZE/2,0,BOX_SIZE/2],[-BOX_SIZE/2,0,BOX_SIZE/2]], dtype=np.float64)) +ground_indices.from_numpy(np.array([0,1,2,0,2,3], dtype=np.int32)) +ground_colors.fill(ti.Vector([0.8, 0.8, 0.8], dt=ti.f32)) + + + +@ti.func +def get_tet_volume(p_indices): + p0, p1, p2, p3 = pos[p_indices[0]], pos[p_indices[1]], pos[p_indices[2]], pos[p_indices[3]] + return (p1 - p0).cross(p2 - p0).dot(p3 - p0) / 6.0 + +@ti.func +def get_barycentric_coords(p, a, b, c, d): + mat = ti.Matrix.cols([a - d, b - d, c - d]) + weights = ti.Vector([0.0, 0.0, 0.0]) + if abs(mat.determinant()) > 1e-9: + weights = mat.inverse() @ (p - d) + w4 = 1.0 - weights.sum() + return ti.Vector([weights[0], weights[1], weights[2], w4]) + +@ti.func +def get_grid_cell(p): + return ti.max(0, ti.min(GRID_SIZE - 1, ti.floor(p * inv_cell_spacing, ti.i32))) + +@ti.func +def clamp_to_box(p): + """Clamp a position to stay within the collision box bounds.""" + return ti.Vector([ + ti.max(box_min[0], ti.min(box_max[0], p[0])), + ti.max(box_min[1], ti.min(box_max[1], p[1])), + ti.max(box_min[2], ti.min(box_max[2], p[2])) + ]) + +@ti.kernel +def init_physics(): + for i in range(num_edges): + id0, id1 = edge_ids[i, 0], edge_ids[i, 1] + edge_lengths[i] = (pos[id0] - pos[id1]).norm() + + inv_mass.fill(0.0) + for i in range(num_tets): + p_indices = ti.Vector([tet_ids[i, 0], tet_ids[i, 1], tet_ids[i, 2], tet_ids[i, 3]]) + vol = get_tet_volume(p_indices) + rest_vol[i] = vol + if vol > 0.0: + p_inv_mass = 1.0 / (vol / 4.0) + for j in ti.static(range(4)): + inv_mass[p_indices[j]] += p_inv_mass + + for i in range(num_particles): + pos[i] += ti.Vector([0.0, 1.0, 0.0]) + prev_pos[i] = pos[i] + vel[i] = ti.Vector([0.0, 0.0, 0.0]) + + +def build_hash_grid(): + """Multi-step process to build the spatial hash grid.""" + grid_cell_counts.fill(0) + + @ti.kernel + def count_verts_in_cells(): + for i in range(num_vis_verts): + cell = get_grid_cell(vis_mesh_rest_pos[i]) + ti.atomic_add(grid_cell_counts[cell], 1) + + count_verts_in_cells() + + total_verts = 0 + counts_np = grid_cell_counts.to_numpy() + starts_np = np.zeros_like(counts_np) + # This prefix sum must be done serially on the CPU. + for i in range(GRID_SIZE): + for j in range(GRID_SIZE): + for k in range(GRID_SIZE): + starts_np[i, j, k] = total_verts + total_verts += counts_np[i, j, k] + grid_cell_starts.from_numpy(starts_np) + + write_offsets = ti.field(ti.i32, shape=(GRID_SIZE, GRID_SIZE, GRID_SIZE)) + write_offsets.copy_from(grid_cell_starts) + + @ti.kernel + def fill_sorted_ids(): + for i in range(num_vis_verts): + cell = get_grid_cell(vis_mesh_rest_pos[i]) + write_idx = ti.atomic_add(write_offsets[cell], 1) + sorted_vis_vert_ids[write_idx] = i + + fill_sorted_ids() + +@ti.kernel +def compute_skinning_info_hashed(): + min_dist.fill(1e9) + skinning_info_tet_idx.fill(-1) + + for tet_idx in range(num_tets): + p_indices = ti.Vector([tet_ids[tet_idx, 0], tet_ids[tet_idx, 1], tet_ids[tet_idx, 2], tet_ids[tet_idx, 3]]) + p0, p1, p2, p3 = pos[p_indices[0]], pos[p_indices[1]], pos[p_indices[2]], pos[p_indices[3]] + + min_coord = min(p0, p1, p2, p3) - CELL_SPACING + max_coord = max(p0, p1, p2, p3) + CELL_SPACING + min_cell, max_cell = get_grid_cell(min_coord), get_grid_cell(max_coord) + + for i, j, k in ti.ndrange( + (min_cell[0], max_cell[0] + 1), (min_cell[1], max_cell[1] + 1), (min_cell[2], max_cell[2] + 1)): + + start, end = grid_cell_starts[i, j, k], grid_cell_starts[i, j, k] + grid_cell_counts[i, j, k] + + for vert_offset in range(start, end): + vis_vert_idx = sorted_vis_vert_ids[vert_offset] + p_vis = vis_mesh_rest_pos[vis_vert_idx] + + bary = get_barycentric_coords(p_vis, p0, p1, p2, p3) + dist = 0.0 + for c in ti.static(range(4)): dist = max(dist, -bary[c]) + + if dist < ti.atomic_min(min_dist[vis_vert_idx], dist): + skinning_info_tet_idx[vis_vert_idx] = tet_idx + skinning_info_bary_weights[vis_vert_idx] = ti.Vector([bary[0], bary[1], bary[2]]) + +@ti.kernel +def update_vis_mesh(): + for i in range(num_vis_verts): + tet_idx = skinning_info_tet_idx[i] + if tet_idx < 0: + vis_mesh_pos[i] = vis_mesh_rest_pos[i] + continue + p_indices = ti.Vector([tet_ids[tet_idx, 0], tet_ids[tet_idx, 1], tet_ids[tet_idx, 2], tet_ids[tet_idx, 3]]) + p0, p1, p2, p3 = pos[p_indices[0]], pos[p_indices[1]], pos[p_indices[2]], pos[p_indices[3]] + b = skinning_info_bary_weights[i] + b3 = 1.0 - b.sum() + vis_mesh_pos[i] = b[0] * p0 + b[1] * p1 + b[2] * p2 + b3 * p3 + +@ti.kernel +def pre_solve(dt: ti.f64, use_gravity: ti.i32): + for i in range(num_particles): + if inv_mass[i] == 0.0: continue + if use_gravity != 0: + vel[i] += gravity * dt + prev_pos[i] = pos[i] + pos[i] += vel[i] * dt + + # Box collision - clamp position to box bounds + pos[i] = clamp_to_box(pos[i]) + +@ti.kernel +def solve_edges(compliance: ti.f64, dt: ti.f64): + alpha = compliance / (dt * dt) + for i in range(num_edges): + id0, id1 = edge_ids[i, 0], edge_ids[i, 1] + w0, w1 = inv_mass[id0], inv_mass[id1] + w_sum = w0 + w1 + if w_sum == 0.0: continue + delta = pos[id0] - pos[id1] + dist = delta.norm() + if dist == 0.0: continue + grad = delta / dist + C = dist - edge_lengths[i] + s = -C / (w_sum + alpha) + pos[id0] += s * w0 * grad + pos[id1] -= s * w1 * grad + +@ti.kernel +def solve_volumes(compliance: ti.f64, dt: ti.f64): + alpha = compliance / (dt * dt) + for i in range(num_tets): + p_indices = ti.Vector([tet_ids[i, 0], tet_ids[i, 1], tet_ids[i, 2], tet_ids[i, 3]]) + w_sum = 0.0 + grads = ti.Matrix.zero(ti.f64, 4, 3) + for j in ti.static(range(4)): + ids = ti.Vector([p_indices[vol_id_order[j][c]] for c in range(3)]) + p0, p1, p2 = pos[ids[0]], pos[ids[1]], pos[ids[2]] + grad = (p1 - p0).cross(p2 - p0) / 6.0 + grads[j, :] = grad + w_sum += inv_mass[p_indices[j]] * grad.norm_sqr() + if w_sum == 0.0: continue + C = get_tet_volume(p_indices) - rest_vol[i] + s = -C / (w_sum + alpha) + for j in ti.static(range(4)): + pos[p_indices[j]] += s * inv_mass[p_indices[j]] * grads[j, :] + +@ti.kernel +def post_solve(dt: ti.f64): + for i in range(num_particles): + if inv_mass[i] == 0.0: continue + vel[i] = (pos[i] - prev_pos[i]) / dt + +def substep(): + pre_solve(sdt, 1) + for _ in range(solver_iterations): + solve_edges(edge_compliance, sdt) + solve_volumes(vol_compliance, sdt) + post_solve(sdt) + +print("Building spatial hash grid for skinning...") +start_time = time.time() +build_hash_grid() +end_time = time.time() +print(f"Hash grid built in {end_time - start_time:.4f} seconds.") + +print("Computing skinning information with hash grid...") +start_time = time.time() +compute_skinning_info_hashed() +end_time = time.time() +print(f"Skinning computation finished in {end_time - start_time:.4f} seconds.") + +init_physics() + +# 2. Setup UI and Camera +window = ti.ui.Window("Taichi XPBD - Dragon Simulation", (1024, 1024), vsync=True) +canvas = window.get_canvas() +scene = window.get_scene() +camera = ti.ui.Camera() +camera.position(0, 1.5, 4.5) +camera.lookat(0, 0.5, 0) + +# 3. Main simulation and rendering loop +while window.running: + gui = window.GUI + with gui.sub_window("Controls", 0.05, 0.05, 0.3, 0.25): + paused = gui.checkbox("Paused", paused) + + gui.text("Animation Export:") + export_enabled = gui.checkbox("Export Animation", export_enabled) + + if export_enabled and usd_exporter is None: + usd_exporter = USDExporter("dragon_animation.usd", fps=60, scale=1.0) + print("USD exporter initialized!") + + edge_compliance_slider = gui.slider_float("Edge Compliance", edge_compliance_slider, 0.0, 50.0) + edge_compliance = edge_compliance_slider + vol_compliance = gui.slider_float("Volume Compliance", vol_compliance, 0.0, 10.0) + + gui.text(f"Exported Frames: {export_frame_count}") + if usd_exporter: + gui.text(f"USD File: {usd_exporter.output_path}") + + if gui.button("Reset"): + pos.from_numpy(mesh["sim_verts"]) + init_physics() + export_frame_count = 0 + if usd_exporter: + usd_exporter = None + + if not paused: + for _ in range(num_substeps): + substep() + + # Update visual mesh before rendering + update_vis_mesh() + + # Export mesh frame if enabled + if export_enabled and not paused and usd_exporter: + # Get current mesh data + vertices = vis_mesh_pos.to_numpy() + faces = vis_mesh_indices.to_numpy().reshape((-1, 3)) + + # Export the frame to USD + usd_exporter.export_frame(vertices, faces) + export_frame_count += 1 + + # Rendering + camera.track_user_inputs(window, movement_speed=0.03, hold_key=ti.ui.RMB) + scene.set_camera(camera) + scene.ambient_light((0.5, 0.5, 0.5)) + scene.point_light(pos=(2, 3, 4), color=(1, 1, 1)) + + scene.mesh(vis_mesh_pos, indices=vis_mesh_indices, per_vertex_color=vis_mesh_colors) + scene.mesh(ground_vertices, indices=ground_indices, per_vertex_color=ground_colors) + + canvas.scene(scene) + window.show() + +# Save USD file when simulation ends +if usd_exporter and export_frame_count > 0: + usd_exporter.save() + print(f"\nAnimation export complete!") + print(f"Total frames exported: {export_frame_count}") + print(f"USD file: {usd_exporter.output_path}") + print(f"\nTo import into Blender:") + print(f"1. File > Import > Universal Scene Description (.usd)") + print(f"2. Select '{usd_exporter.output_path}'") + print(f"3. The animation will be imported as a single animated sequence!") diff --git a/14_pbf/simulator.py b/14_pbf/simulator.py new file mode 100644 index 0000000..afb9293 --- /dev/null +++ b/14_pbf/simulator.py @@ -0,0 +1,519 @@ + +import math +import numpy as np +import taichi as ti + +ti.init(arch=ti.gpu, default_fp=ti.f32) + +SUBSTEPS_PER_FRAME = 2 + +dim = 3 +screen_res = (800, 800) +screen_to_world_ratio = 20.0 +boundary = (screen_res[0] / screen_to_world_ratio * 2.2, + screen_res[1] / screen_to_world_ratio * 1.0, + screen_res[0] / screen_to_world_ratio * 1.0) + +cell_size = 1.8 + +cell_recpr = 1.0 / cell_size + +def round_up(f, s): + return (math.floor(f * cell_recpr / s) + 1) * s + +grid_size = (round_up(boundary[0], 1), round_up(boundary[1], 1), round_up(boundary[2], 1)) + +num_particles = 100000 +max_num_particles_per_cell = 100 +max_num_neighbors = 100 +time_delta = 1.0 / 30.0 +epsilon = 1e-5 + +particle_radius = 4.0 +particle_radius_in_world = particle_radius / screen_to_world_ratio + +particle_color = (0.4, 0.7, 1.0) +boundary_color = (0.9, 0.7, 0.6) + +h = 1.1 +mass = 1.0 +rho0 = 1.0 +lambda_epsilon = 50.0 +pbf_num_iters = 7 +corr_deltaQ_coeff = 0.3 +corrK = 0.001 +neighbor_radius = h * 1.05 +xsph_viscosity_c = 0.01 +vorticity_epsilon = 0.01 + +poly6_factor = 315.0 / (64.0 * math.pi) +spiky_grad_factor = -45.0 / math.pi + +old_positions = ti.Vector.field(dim, float, shape=num_particles) +positions = ti.Vector.field(dim, float, shape=num_particles) +velocities = ti.Vector.field(dim, float, shape=num_particles) +grid_num_particles = ti.field(int, shape=grid_size) +grid2particles = ti.field(int, shape=(*grid_size, max_num_particles_per_cell)) +particle_num_neighbors = ti.field(int, shape=num_particles) +particle_neighbors = ti.field(int, shape=(num_particles, max_num_neighbors)) +lambdas = ti.field(float, shape=num_particles) +position_deltas = ti.Vector.field(dim, float, shape=num_particles) +velocity_deltas_xsph = ti.Vector.field(dim, float, shape=num_particles) +wall_states = ti.Vector.field(3, float, shape=()) +particle_colors = ti.Vector.field(3, float, shape=num_particles) +vorticity = ti.Vector.field(dim, float, shape=num_particles) +vorticity_force = ti.Vector.field(dim, float, shape=num_particles) +wall_moving = ti.field(bool, shape=()) +simulation_running = ti.field(bool, shape=()) + + +@ti.func +def poly6_value(s, h_): + result = 0.0 + if 0 < s and s < h_: + x = (h_ * h_ - s * s) / (h_ * h_ * h_) + result = poly6_factor * x * x * x + return result + +@ti.func +def spiky_gradient(r, h_): + result = ti.Vector([0.0, 0.0, 0.0]) + r_len = r.norm() + if 0 < r_len and r_len < h_: + x = (h_ - r_len) / (h_ * h_ * h_) + g_factor = spiky_grad_factor * x * x + result = r * g_factor / r_len + return result + +@ti.func +def compute_scorr(pos_ji): + x = poly6_value(pos_ji.norm(), h) / poly6_value(corr_deltaQ_coeff * h, h) + x = x * x; x = x * x + return -corrK * x + +@ti.func +def get_cell(pos): + return int(pos * cell_recpr) + +@ti.func +def is_in_grid(c): + return 0 <= c[0] < grid_size[0] and 0 <= c[1] < grid_size[1] and 0 <= c[2] < grid_size[2] + +@ti.func +def confine_position_to_boundary(p): + left_wall_x = wall_states[None][0] + right_wall_x = wall_states[None][1] + bmax = ti.Vector([right_wall_x, boundary[1], boundary[2]]) - particle_radius_in_world + bmin = ti.Vector([left_wall_x, 0.0, 0.0]) + particle_radius_in_world + for i in ti.static(range(dim)): + if p[i] <= bmin[i]: + p[i] = bmin[i] + epsilon * ti.random() + elif p[i] >= bmax[i]: + p[i] = bmax[i] - epsilon * ti.random() + return p + +@ti.kernel +def pre_solve(): + for i in positions: + old_positions[i] = positions[i] + + for i in positions: + g = ti.Vector([0.0, -9.8, 0.0]) + vel = velocities[i] + g * time_delta + velocities[i] = vel + positions[i] = positions[i] + vel * time_delta + + grid_num_particles.fill(0) + + for p_i in positions: + cell = get_cell(positions[p_i]) + offs = ti.atomic_add(grid_num_particles[cell], 1) + if offs < max_num_particles_per_cell: + grid2particles[cell, offs] = p_i + + for p_i in positions: + pos_i = positions[p_i] + cell = get_cell(pos_i) + nb_i = 0 + for offs in ti.static(ti.grouped(ti.ndrange((-1, 2), (-1, 2), (-1, 2)))): + cell_to_check = cell + offs + if is_in_grid(cell_to_check): + for j in range(grid_num_particles[cell_to_check]): + p_j = grid2particles[cell_to_check, j] + if nb_i < max_num_neighbors and p_j != p_i and (pos_i - positions[p_j]).norm() < neighbor_radius: + particle_neighbors[p_i, nb_i] = p_j + nb_i += 1 + particle_num_neighbors[p_i] = nb_i + +@ti.kernel +def solve_density_constraints(): + for p_i in positions: + pos_i = positions[p_i] + grad_i, sum_gradient_sqr, density_constraint = ti.Vector([0.0, 0.0, 0.0]), 0.0, 0.0 + + for j in range(particle_num_neighbors[p_i]): + p_j = particle_neighbors[p_i, j] + pos_ji = pos_i - positions[p_j] + grad_j = spiky_gradient(pos_ji, h) + grad_i += grad_j + sum_gradient_sqr += grad_j.dot(grad_j) + density_constraint += poly6_value(pos_ji.norm(), h) + + density_constraint = (mass * density_constraint / rho0) - 1.0 + sum_gradient_sqr += grad_i.dot(grad_i) + + denominator = (1.0 / mass) * sum_gradient_sqr + lambda_epsilon + # lambdas[p_i] = -density_constraint / (sum_gradient_sqr + lambda_epsilon) + lambdas[p_i] = -density_constraint / denominator if denominator > epsilon else 0.0 + + for p_i in positions: + pos_i = positions[p_i] + lambda_i = lambdas[p_i] + pos_delta_i = ti.Vector([0.0, 0.0, 0.0]) + + for j in range(particle_num_neighbors[p_i]): + p_j = particle_neighbors[p_i, j] + lambda_j = lambdas[p_j] + pos_ji = pos_i - positions[p_j] + scorr_ij = compute_scorr(pos_ji) + pos_delta_i += (lambda_i + lambda_j + scorr_ij) * spiky_gradient(pos_ji, h) + + position_deltas[p_i] = pos_delta_i / rho0 + + for i in positions: + positions[i] += position_deltas[i] + +@ti.kernel +def calculate_vorticity(): + for i in positions: + vort_i = ti.Vector([0.0, 0.0, 0.0]) + for j in range(particle_num_neighbors[i]): + p_j = particle_neighbors[i, j] + pos_ji = positions[i] - positions[p_j] + + # Relative velocity: v_ij = v_j - v_i + vel_ij = velocities[p_j] - velocities[i] + + # Cross product of relative velocity and spiky gradient + vort_i += vel_ij.cross(spiky_gradient(pos_ji, h)) + + vorticity[i] = vort_i + +@ti.kernel +def apply_vorticity_confinement(): + # 1. Calculate the corrective force `f_vorticity` for each particle + for i in positions: + # First, calculate eta = \nabla|\omega| + # This is the gradient of the magnitude of the vorticity field. + eta = ti.Vector([0.0, 0.0, 0.0]) + vort_i_norm = vorticity[i].norm() + + for j in range(particle_num_neighbors[i]): + p_j = particle_neighbors[i, j] + pos_ji = positions[i] - positions[p_j] + + vort_j_norm = vorticity[p_j].norm() + + # Difference in vorticity magnitude multiplied by the kernel gradient + eta += (vort_j_norm - vort_i_norm) * spiky_gradient(pos_ji, h) + + # Calculate the direction vector N = eta / |eta| + eta_norm = eta.norm() + if eta_norm > epsilon: # Avoid division by zero + N = eta / eta_norm + # Calculate the final force: f_vorticity = epsilon * (N x omega_i) + vorticity_force[i] = vorticity_epsilon * N.cross(vorticity[i]) + else: + vorticity_force[i] = ti.Vector([0.0, 0.0, 0.0]) + + # 2. Apply the calculated force to the velocities + for i in velocities: + # The paper applies a force, so we integrate it over the timestep + velocities[i] += vorticity_force[i] * time_delta + +@ti.kernel +def apply_xsph_viscosity(): + # 1. Calculate velocity corrections in parallel + for i in positions: + vel_i = velocities[i] + delta_v = ti.Vector([0.0, 0.0, 0.0]) + for j in range(particle_num_neighbors[i]): + p_j = particle_neighbors[i, j] + pos_ji = positions[i] - positions[p_j] + vel_ij = velocities[p_j] - vel_i + w_ij = poly6_value(pos_ji.norm(), h) + delta_v += vel_ij * w_ij + velocity_deltas_xsph[i] = xsph_viscosity_c * delta_v + + # 2. Apply corrections + for i in positions: + velocities[i] += velocity_deltas_xsph[i] + +@ti.kernel +def post_solve(): + for i in positions: + positions[i] = confine_position_to_boundary(positions[i]) + + for i in positions: + velocities[i] = (positions[i] - old_positions[i]) / time_delta + +def substep(): + if simulation_running[None]: + pre_solve() + for _ in range(pbf_num_iters): + solve_density_constraints() + post_solve() + + calculate_vorticity() + apply_vorticity_confinement() + apply_xsph_viscosity() + +@ti.kernel +def init_particles(): + padding = particle_radius_in_world + + for i in range(num_particles): + x = padding + ti.random() * (boundary[0] - 2 * padding) + y = padding + ti.random() * (boundary[1] - 2 * padding) + z = padding + ti.random() * (boundary[2] - 2 * padding) + + positions[i] = ti.Vector([x, y, z]) + velocities[i] = ti.Vector([0.0, 0.0, 0.0]) + + wall_states[None] = ti.Vector([epsilon, boundary[0] - epsilon, 0.0]) + +@ti.kernel +def update_particle_colors(): + max_velocity = 10.0 + + blue = ti.Vector([0.0941, 0.2784, 0.6314]) + teal = ti.Vector([0.1392, 0.7226, 0.5441]) + yellow = ti.Vector([0.9922, 0.9216, 0.0431]) + red = ti.Vector([0.9804, 0.1961, 0.0196]) + + for i in positions: + vel_magnitude = velocities[i].norm() + normalized_vel = ti.min(vel_magnitude / max_velocity, 1.0) + + if normalized_vel < 0.35: + t = normalized_vel / 0.35 + particle_colors[i] = blue + t * (teal - blue) + elif normalized_vel < 0.65: + t = (normalized_vel - 0.35) / 0.30 + particle_colors[i] = teal + t * (yellow - teal) + elif normalized_vel < 0.85: + t = (normalized_vel - 0.65) / 0.20 + particle_colors[i] = yellow + t * (red - yellow) + else: + particle_colors[i] = red + +@ti.kernel +def move_wall(speed_multiplier: float): + w = wall_states[None] + + if wall_moving[None] and simulation_running[None]: + w[2] += speed_multiplier + period = 90 + vel_strength = 5.0 + movement_time = w[2] + if movement_time >= 2 * period: + w[2] = 0 + movement_time = 0 + + movement_offset = ti.sin(movement_time * 3.14159 / period) * vel_strength * time_delta * speed_multiplier + + w[0] += movement_offset + w[1] -= movement_offset + + w[0] = ti.max(w[0], epsilon) + w[1] = ti.min(w[1], boundary[0] - epsilon) + else: + w[0] = epsilon + w[1] = boundary[0] - epsilon + w[2] = 0 + + wall_states[None] = w + +def create_box_edges(): + left_wall_x = wall_states[None][0] + right_wall_x = wall_states[None][1] + + corners = [ + [left_wall_x, 0.0, 0.0], + [right_wall_x, 0.0, 0.0], + [right_wall_x, boundary[1], 0.0], + [left_wall_x, boundary[1], 0.0], + [left_wall_x, 0.0, boundary[2]], + [right_wall_x, 0.0, boundary[2]], + [right_wall_x, boundary[1], boundary[2]], + [left_wall_x, boundary[1], boundary[2]] + ] + + edges = [ + [0, 1], [1, 2], [2, 3], [3, 0], + [4, 5], [5, 6], [6, 7], [7, 4], + [0, 4], [1, 5], [2, 6], [3, 7] + ] + + return corners, edges + +def create_original_box_edges(): + left_wall_x = epsilon + right_wall_x = boundary[0] - epsilon + + corners = [ + [left_wall_x, 0.0, 0.0], + [right_wall_x, 0.0, 0.0], + [right_wall_x, boundary[1], 0.0], + [left_wall_x, boundary[1], 0.0], + [left_wall_x, 0.0, boundary[2]], + [right_wall_x, 0.0, boundary[2]], + [right_wall_x, boundary[1], boundary[2]], + [left_wall_x, boundary[1], boundary[2]] + ] + edges = [ + [0, 1], [1, 2], [2, 3], [3, 0], + [4, 5], [5, 6], [6, 7], [7, 4], + [0, 4], [1, 5], [2, 6], [3, 7] + ] + return corners, edges + +def main(): + global SUBSTEPS_PER_FRAME + + particle_color = (0.4, 0.7, 1.0) + boundary_color = (0.9, 0.7, 0.6) + + wall_moving[None] = False + simulation_running[None] = False + + fps_counter = 0 + fps_timer = 0.0 + current_fps = 0.0 + + init_particles() + update_particle_colors() + window = ti.ui.Window("PBF3D with XSPH Viscosity", screen_res, vsync=True) + canvas = window.get_canvas() + scene = window.get_scene() + camera = ti.ui.Camera() + gui = window.get_gui() + + cam_pos = ti.Vector([20.0, 25.0, 120.0]) + cam_yaw = 0.0 + cam_pitch = 0.0 + cam_move_speed = 1.5 + cam_rot_speed = 0.02 + + def get_forward(): + cy = math.cos(cam_yaw); sy = math.sin(cam_yaw) + cp = math.cos(cam_pitch); sp = math.sin(cam_pitch) + return ti.Vector([sy * cp, -sp, -cy * cp]) + + def get_right(): + f = get_forward() + up = ti.Vector([0.0, 1.0, 0.0]) + r = f.cross(up) + n = r.norm() + return r / (n if n > 1e-8 else 1.0) + + def get_up(): + r = get_right() + f = get_forward() + return r.cross(f) * -1.0 + + + while window.running: + fps_counter += 1 + fps_timer += time_delta + if fps_timer >= 1.0: + current_fps = fps_counter / fps_timer + fps_counter = 0 + fps_timer = 0.0 + + gui.begin("Simulation Controls", 0.05, 0.05, 0.3, 0.2) + + gui.text(f"FPS: {current_fps:.1f}") + gui.text(f"Substeps per frame: {SUBSTEPS_PER_FRAME}") + gui.text(f"Effective simulation speed: {SUBSTEPS_PER_FRAME}x") + gui.text(f"Wall movement: Synchronized") + + gui.text("Performance:") + if gui.button("1x Speed (1 substep)"): + SUBSTEPS_PER_FRAME = 1 + if gui.button("2x Speed (2 substeps)"): + SUBSTEPS_PER_FRAME = 2 + if gui.button("3x Speed (3 substeps)"): + SUBSTEPS_PER_FRAME = 3 + if gui.button("4x Speed (4 substeps)"): + SUBSTEPS_PER_FRAME = 4 + + if gui.button("Run Simulation"): + simulation_running[None] = True + wall_moving[None] = True + + gui.end() + + if simulation_running[None]: + move_wall(SUBSTEPS_PER_FRAME) + + for _ in range(SUBSTEPS_PER_FRAME): + substep() + + update_particle_colors() + + if window.is_pressed(ti.ui.LEFT): + cam_yaw -= cam_rot_speed + if window.is_pressed(ti.ui.RIGHT): + cam_yaw += cam_rot_speed + if window.is_pressed(ti.ui.UP): + cam_pitch = max(cam_pitch - cam_rot_speed, -1.4) + if window.is_pressed(ti.ui.DOWN): + cam_pitch = min(cam_pitch + cam_rot_speed, 1.4) + + move = ti.Vector([0.0, 0.0, 0.0]) + if window.is_pressed('w'): + move += get_forward() + if window.is_pressed('s'): + move -= get_forward() + if window.is_pressed('a'): + move -= get_right() + if window.is_pressed('d'): + move += get_right() + if window.is_pressed('q'): + move -= ti.Vector([0.0, 1.0, 0.0]) + if window.is_pressed('e'): + move += ti.Vector([0.0, 1.0, 0.0]) + if move.norm() > 1e-8: + move = move / move.norm() + cam_pos += move * cam_move_speed + + cam_forward = get_forward() + cam_target = cam_pos + cam_forward + camera.position(cam_pos[0], cam_pos[1], cam_pos[2]) + camera.lookat(cam_target[0], cam_target[1], cam_target[2]) + + scene.set_camera(camera) + scene.ambient_light((0.5, 0.5, 0.5)) + scene.point_light(pos=(30, 30, 30), color=(1, 1, 1)) + + scene.particles(positions, radius=particle_radius_in_world, per_vertex_color=particle_colors) + + orig_corners, orig_edges = create_original_box_edges() + for i in range(12): + start_corner = np.array(orig_corners[orig_edges[i][0]], dtype=np.float32) + end_corner = np.array(orig_corners[orig_edges[i][1]], dtype=np.float32) + scene.lines(np.array([start_corner, end_corner], dtype=np.float32), color=(0.6, 0.6, 0.6), width=1) + + corners, edges = create_box_edges() + for i in range(12): + start_corner = np.array(corners[edges[i][0]], dtype=np.float32) + end_corner = np.array(corners[edges[i][1]], dtype=np.float32) + scene.lines(np.array([start_corner, end_corner], dtype=np.float32), color=(0.85, 0.85, 0.85), width=2) + + canvas.scene(scene) + + window.show() + +if __name__ == "__main__": + main() \ No newline at end of file