[particles in a box] Animation of particles inside a polygon with additional polygons on the inside. #manim #physics #dt #updater #intersection #collision

20250909_particles.py

            # https://discord.com/channels/581738731934056449/1414961601127383170/1415086069568766024
from manim import *

class dotinbox(Scene):
    def construct(self):
        outerbox = RegularPolygon(n=6).rotate(5*DEGREES).scale_to_fit_height(7)
        innerobjs = VGroup(
            RegularPolygon(n=5, fill_opacity=1).scale_to_fit_height(2).shift(UR),
            Square(side_length=1).shift(DL)
        )
        self.add(outerbox,innerobjs)
        dot = Dot(point=[-1,1,0],color=RED)
        dot.vel = np.array([3,0,0])
        def dotupdater(mobj,dt):
            mobj.shift(dt*mobj.vel)
            ins = Intersection(outerbox,mobj)
            if ((ins.width*ins.height) < (mobj.width*mobj.height)/2):
                mp = mobj.get_center()
                mobj.shift(-dt*mobj.vel)
                vsdiff = [v - mp for v in outerbox.get_vertices()]
                vsdiff.sort(key=np.linalg.norm)
                norm = np.array([[0,-1,0],[1,0,0],[0,0,0]]) @ (vsdiff[1]-vsdiff[0])
                projNV = ((mobj.vel @ norm)/(norm @ norm)) * norm
                mobj.vel = mobj.vel - 2*projNV
                mobj.shift(dt*mobj.vel)

            for inner in innerobjs:
                ins = Intersection(inner,mobj)
                if ((ins.width*ins.height) > (mobj.width*mobj.height)/2):
                    mp = mobj.get_center()
                    mobj.shift(-dt*mobj.vel)
                    vsdiff = [v - mp for v in inner.get_vertices()]
                    vsdiff.sort(key=np.linalg.norm)
                    norm = np.array([[0,-1,0],[1,0,0],[0,0,0]]) @ (vsdiff[1]-vsdiff[0])
                    projNV = ((mobj.vel @ norm)/(norm @ norm)) * norm
                    mobj.vel = mobj.vel - 2*projNV
                    mobj.shift(dt*mobj.vel)
        dot.add_updater(dotupdater)
        dots = VGroup(
            dot.copy().set_color(np.random.choice([RED,GREEN,YELLOW,TEAL,BLUE,ORANGE]))
            for _ in range(10)
        )
        for d in dots:
            d.vel = np.array([np.random.uniform(-2,2),np.random.uniform(-2,2),0])
        self.add(dots)
        self.wait(25)

20250910_particle.py

# possibly improved version

class dotsbox(Scene):
    def construct(self):
        obox = RegularPolygon(n=6).rotate(5*DEGREES).scale_to_fit_height(7)
        iobjs = VGroup(
            RegularPolygon(n=5, fill_opacity=1).scale_to_fit_height(2).shift(UR),
            Square(side_length=1).shift(DL)
        )
        self.add(obox,iobjs)
        dot = Dot(point=[-1,1,0],color=RED)
        dot.vel = np.array([3,0,0])
        def dupd(mobj,dt):
            mobj.shift(dt*mobj.vel)
            ins = Intersection(obox,mobj)
            if ((ins.width*ins.height) < (mobj.width*mobj.height)*.75):
                mobj.shift(-dt*mobj.vel)
                mp = mobj.get_center()
                dif = [v - mp for v in obox.get_vertices()]
                dif.sort(key=np.linalg.norm)
                norm = np.array([[0,-1,0],[1,0,0],[0,0,0]]) @ (dif[1]-dif[0])
                pNV = ((mobj.vel @ norm)/(norm @ norm)) * norm
                mobj.vel = mobj.vel - 2*pNV
                mobj.shift(dt*mobj.vel)

            for i in iobjs:
                ins = Intersection(i,mobj)
                if ((ins.width*ins.height) > (mobj.width*mobj.height)/100):
                    mobj.shift(-dt*mobj.vel)
                    mp = mobj.get_center()
                    dif = [v - mp for v in i.get_vertices()]
                    dif.sort(key=np.linalg.norm)
                    norm = np.array([[0,-1,0],[1,0,0],[0,0,0]]) @ (dif[1]-dif[0])
                    pNV = ((mobj.vel @ norm)/(norm @ norm)) * norm
                    mobj.vel = mobj.vel - 2*pNV
                    mobj.shift(dt*mobj.vel)
        dot.add_updater(dupd)
        dots = VGroup(
            dot.copy().set_color(np.random.choice([RED,GREEN,YELLOW,TEAL,BLUE,ORANGE]))
            for _ in range(10)
        )
        for d in dots:
            d.vel = np.array([np.random.uniform(-2,2),np.random.uniform(-2,2),0])
        self.add(dots)
        self.play(Rotate(iobjs[0],5*PI),rate_func=rate_functions.linear,run_time=25)

readme.md

Collision detection by means of the intersection of the bouncing objects and the boundary objects with different inner and outer boundary objects.

for the calculation of the reflected vector https://www.contemporarycalculus.com/dh/Calculus_all/CC11_7_VectorReflections.pdf

some remaining problems with particles sometimes tunneling into the inner objects

scriptoutput.mp4