Homework 0 rope simulator

GAMES201 高级物理引擎课程专区
#1

小白水平有限因此仿写了GAMES101的作业8，用的是半隐式欧拉法。上周还没写完这周还没看lect.02，不知道会不会有什么错误，请大家帮忙运行看看。

代码如下：

# rope_simulator.py

import taichi as ti

ti.init(arch=ti.gpu)

n = 320
image = ti.var(dt=ti.f32, shape=(n * 2, n))
# 10个质点
# 各质点位置
positions = ti.Vector(2, dt=ti.f32, shape=10)
# 各质点受力
forces = ti.Vector(2, dt=ti.f32, shape=10)
# 各质点速度
velocities = ti.Vector(2, dt=ti.f32, shape=10)
# 重力加速度
gravity = ti.Vector([0, -1])
# 原长
rest_length = ti.var(dt=ti.f32, shape=())
# 弹簧系数
k = ti.var(dt=ti.f32, shape=())
# 质点质量
mass = ti.var(dt=ti.f32, shape=())
# 步长
delta_t = ti.var(dt=ti.f32, shape=())

def my_abs(x):
    if x < 0:
        return -x
    else:
        return x


@ti.func
def draw_line(a, b):
    x0 = a[0]
    x1 = b[0]
    y0 = a[1]
    y1 = b[1]
    steep = False
    if my_abs(x0 - x1) < my_abs(y0 - y1):
        temp = x0
        x0 = y0
        y0 = temp
        temp = x1
        x1 = y1
        y1 = temp
        steep = True
    if x0 > x1:
        temp = x0
        x0 = x1
        x1 = temp
        temp = y0
        y0 = y1
        y1 = temp
    for x in range(x0, x1):
        t = (x - x0) / (x1 - x0)
        y = y0 + (y1 - y0) * t
        if steep:
            image[ti.cast(y, ti.i32), ti.cast(x, ti.i32)] = 0.3
        else:
            image[ti.cast(x, ti.i32), ti.cast(y, ti.i32)] = 0.3


@ti.kernel
def init():
    rest_length[None] = 20
    k[None] = 100
    mass[None] = 1
    delta_t[None] = 1 / 16
    for i in range(10):
        positions[i] = [220 + i * rest_length[None], 280]


@ti.kernel
def update():
    for i, j in image:
        image[i, j] = 0
    for i in range(9):
        b_a = positions[i + 1] - positions[i]
        fb_a = -k[None] * b_a * (b_a.norm() - rest_length[None]) / b_a.norm()
        forces[i] -= fb_a
        forces[i + 1] += fb_a
    for i in range(1, 10):
        forces[i] += mass[None] * gravity
        accel = forces[i] / mass[None]
        cur_velocity = velocities[i] + accel * delta_t[None]

        forces[i] -= 0.005 * cur_velocity
        accel = forces[i] / mass[None]

        velocities[i] += accel * delta_t[None]
        positions[i] += velocities[i] * delta_t[None]
    for force in forces:
        forces[force] = [0, 0]
    for i in range(9):
        draw_line(positions[i], positions[i + 1])
    for i in range(10):
        image[ti.cast(positions[i][0], ti.i32), ti.cast(positions[i][1], ti.i32)] = 1


gui = ti.GUI("Rope Simulator", (n * 2, n))

init()
for i in range(100000000):
    update()
    gui.set_image(image)
    gui.show()
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#2

跑了一下很强！

#3

我来上个图：

video

感觉可以调一下背景颜色和弹簧、质点粗细。

#4

Taichi GUI可以直接用来画line, circle等功能哈。

#5

rope
根据老师和助教的建议修改了下。

# rope_simulator.py

import taichi as ti
import numpy as np

ti.init(arch=ti.gpu)

w = 640
h = 480
# 10个质点
# 各质点位置
positions = ti.Vector(2, dt=ti.f32, shape=10)
draw_positions = ti.Vector(2, dt=ti.f32, shape=10)
# 各质点受力
forces = ti.Vector(2, dt=ti.f32, shape=10)
# 各质点速度
velocities = ti.Vector(2, dt=ti.f32, shape=10)
# 重力加速度
gravity = ti.Vector([0, -1])
# 原长
rest_length = ti.var(dt=ti.f32, shape=())
# 弹簧系数
k = ti.var(dt=ti.f32, shape=())
# 质点质量
mass = ti.var(dt=ti.f32, shape=())
# 步长
delta_t = ti.var(dt=ti.f32, shape=())


def my_abs(x):
    if x < 0:
        return -x
    else:
        return x


@ti.kernel
def init():
    rest_length[None] = 30
    k[None] = 100
    mass[None] = 1
    delta_t[None] = 1 / 10
    x = 0.5 * w
    y = 0.8 * h
    for i in range(10):
        positions[i] = [x + i * rest_length[None], y]


@ti.kernel
def update():
    for i in range(9):
        b_a = positions[i + 1] - positions[i]
        fb_a = -k[None] * b_a * (b_a.norm() - rest_length[None]) / b_a.norm()
        forces[i] -= fb_a
        forces[i + 1] += fb_a
    for i in range(10):
        if i:
            forces[i] += mass[None] * gravity
            acceleration = forces[i] / mass[None]
            cur_velocity = velocities[i] + acceleration * delta_t[None]

            forces[i] -= 0.005 * cur_velocity
            acceleration = forces[i] / mass[None]

            velocities[i] += acceleration * delta_t[None]
            positions[i] += velocities[i] * delta_t[None]
        forces[i] = [0, 0]
        draw_positions[i] = positions[i]
    for i in range(10):
        draw_positions[i][0] /= w
        draw_positions[i][1] /= h


gui = ti.GUI("Rope Simulator", (w, h), 0xffffff)

init()
for i in range(100000000):
    for e in gui.get_events(ti.GUI.PRESS):
        if e.key in [ti.GUI.ESCAPE]:
            exit()
    update()
    for i in range(10):
        if i:
            gui.line(begin=[draw_positions[i - 1][0], draw_positions[i - 1][1]],
                     end=[draw_positions[i][0], draw_positions[i][1]],
                     radius=1,
                     color=0xff0000)
        gui.circle(pos=(draw_positions[i][0], draw_positions[i][1]), color=0x0000ff, radius=3)
    gui.text(content="Particles count = 10", pos=(0.001, 0.999), color=0x000000)
    gui.show()
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