Bouncing balls in a heptagon · kimi-k3.1-pro

I need build index self contained physics polished. Should use tools, browser checks. Should plan mentally. Should have exactly 20, compact arrangement non overlap. Rotating heptagon period 5 sec, radius perhaps 310 canvas 760 square responsive. Should be robust. Physics custom fixed substeps, moving wall collision impulse plus wall spin, friction damping, ball ball rotation impulse. Stable.

I'll create. Perhaps screenshot checks reset exact orientation and initial arrangement. Could add deterministic reset, pause. Canvas scales dpr. UI aesthetically polished dark physics lab. Display time, contacts, rotation. User only require. Make sure no extraneous balls. Initial 5x4 perhaps spacing 38, r15 => 5x4 grid width 152 height 114 centered y -30? Canvas square 720? Enclosure R310 ball 16. 5 columns x4 rows spacing 38 => 152x114. Near center. fall gravity 360 px/s². Rotation 2π/5 =1.2566 rad/s, wall tangential speed R~400 causing strong. Should have containment with high wall speed. Ball collision walls polygon moving solid rotation. Implement position-based polygon wall collision, normal inward. For CCW vertices? Canvas coordinates. Construct angles = theta - π/2 + i2π/7, canvas y positive means visually clockwise? Standard canvas x cos y sin so increasing theta rotates clockwise. Fine. Polygon vertices CCW in math but screen positive orientation? Cross sum positive means CCW in canvas? Inward normals can derive via centroid: for each edge nearest point, if ball outside. Simpler signed planes. Vertices ordered increasing angle with y down yields positive cross. For each edge e, interior left side in standard y down? cross(e, center-v) positive for square sequence top -> right etc? Heptagon v at top, next upper-right etc, center-left relative first edge? Edge down-right, to center down-left: cross e x to center = ex*y - ey*x positive? ex+ ey+, x negative y positive => + - (+*-) positive. So inside cross >=0. inward normal =(-ey, ex) normalized gives left normal for edge down-right =(-,+) toward center. Plane distance cross(e,p-v)/len. If distance < r, penetration r-distance; push p += n pen. vn=(v-vwall) dot n, if vn<0 impulse -(1+e)vn. Wall point v=omega cross r: (-ω*ry,ω*rx) for screen clockwise. friction tangent. Pos correction perhaps 1.02. Use slop. collision multiple iterations 2-4. Velocity cap 800.

Ball-ball impulses standard, friction tangent and angular. Should spin visible. Ball spin from contacts. Use angularVel rad/s. Collision response tangent includes surface velocities. Wall relative point velocity ball contact v + rotational surface. For contact at p-r n? normal inward n from wall to center, contact point ball toward wall = -n*r. Surface rotational screen omega: (-w*ry,w*rx), rvec=-r n. tangent t=(-n.y,n.x) perhaps. For relative at contact = v + rotational(-r n) - wallv. Normal vn uses center rel enough. Tangential impulse jt = -vt/(invMass + r²/inertia) clamp mu*jn. Apply v += jt*t/m. w += cross(rcontact, jt*t)/I. Wall not dynamic. Normal impulse also could affect spin no.

Ball-ball: n from a to b, contact ra=r*n, rb=-r*n. Relative at contact = (vb+rot(rb))-(va+rot(ra)). vn = dot(rel,n). if vn<0, normal impulse jn = -(1+e)vn/(2/m + perhaps rotational not needed normal), apply a -=, b+=. Friction with updated tangent rv, jt clamp. Pos corrections equally by overlap. Iterations 3 with collisions. Integrate then solve ball pairs and walls perhaps 4 loops. Fixed dt=1/120 and 3 collision iterations; up to 5 catchup steps per frame? At 60 two steps. Clamp frame delta .04 and accumulator; to avoid slow motion no issue.

Stable wall moving. Should have orientation reset exactly. time=0 theta=0. Pause stops raf updates but draw perhaps overlay. Reset sets running perhaps preserve pause? Best reset running true and pause label Pause. User compare initial screenshot likely click reset and pause quickly. Could provide reset restores and paused? Usually Reset restores and runs. fine. Initial view compact centered at y=-25 and grid numbers row major. Balls colors individual nice hues, radial circles with inner line and rotating number. Render each ball rotate canvas by angle then gradient? gradient rotates harmless. Number rotate exactly. Draw outer ring, small spin marker to visible, number bold. Could number orientation all initially zero.

Background canvas 720x720. Enclosure fully visible R300? canvas coordinate center 360; outer R302, walls stroke 8 plus effect. ball r15.5 initial spacing 38. 5x4. Initial arrangement from x=-76 to76 y=-82? near center. Set y = -74 + row*38 => -74..40. fall. Heptagon center y 360. good.

Enclosure has interior fill, grid/radial decoration outside perhaps no assets. Canvas CSS width min. side panel perhaps header controls at top. Single page. Canvas exactly 20 visible initially. Responsive page 1200x800. Main width 1080 display grid canvas + right telemetry? Canvas 700? Browser screenshot 1200x800 should fit. Header 70, card canvas ~650. At 800 high. Make app max-width 1040, header, stage 680? Side panel 250, canvas width 100%, aspect ratio. Use main layout grid minmax(0, 760) 260, overall 1080. At viewport 1200, content padding 24 => max 1100, stage perhaps 770 + panel. Height 90+730 >800. Set canvas display width 100%, stage grid with canvas-shell; overall 1000 gives left 720? side 240 gaps. header. 720 + margins 40+ header80=840. Better max width 1020 left 720? 1020-260-20=740. too. max 960 left680 +260+20. height ~680+100=780 fits. At 1200x800 yes. Use width min(960, calc100-32). panel. canvas 680. World canvas internal 720. fully visible. On mobile stack.

Perhaps no side excessive, panel controls and live data. Header title "KINETIC / 07" etc. Panel status LIVE, rotation 72.0°/s, gravity, bodies 20, elapsed. Footer small.

Should implement FPS perhaps contacts. Initial status. Keyboard Space pause R reset. Buttons. accessibility.

Canvas resolution use canvas width=720 height=720, CSS responsive and browser handles. Retina? internal fixed 720 enough; use resize DPR perhaps coordinates. Easier set logical W=720 and actual dpr then ctx.setTransform(dpr...). Resize on dpr. canvas width W*dpr. Good.

Potential use Path2D okay no third party. No network.

Should browser test sampling via screenshots and inspect console. Tools browser screenshot only no eval? inspect DOM console. Motion frames perhaps. I can use browser action motion. I'll write file.

Looks good. Should test several moments. Browser motion perhaps motion captures.

Interesting motion tool elapsed jumped 5 sec then frame times mismatch but okay. Visual balls contained mostly perhaps ball at left wall overlap? Looks contact. Should have initial fall from reset and pause. Test pause freeze by inspect screenshot after click then wait? Browser click and motion perhaps pause should no elapsed. click coordinates button 966,154.

Pause working. Should reset compare. Click reset.

Reset good exactly. Perhaps check pause immediately then initial fall at moments. I have tested. Could inspect issue initial balls numbers small but fine. Perhaps physics formula rotation signs check wall collision spin. In ball pair relative formulas suspect incorrect: surface velocity = (-ω*ry, ω*rx). At a ra, surface =(-ω*ray, ω*rax). code a surface (a.vx - a.omega*rax) (uses rax not ray!) and a.vy+a.omega*ray (uses ray not rax) swapped. Similarly b. Yes bug! Wall code rvx=ball.vx-ball.omega*brx correct should -omega*bry. rvy +omega*brx correct. They swapped rvx. I'll fix both pair and wall. Ball pair currently:
rvx=(b.vx-b.omega*rbx)-(a.vx-a.omega*rax) should b.vx - b.omega*rby ; a.vx-a.omega*ray.
rvy correct b.vy+b.omega*rbx, a.vy+a.omega*rax. wall rvx should -omega*bry. This matters spin. Fix. Also torque ball pair a sign: impulse on a is -J, torque cross(ra,-J) = -cross, code -= correct; b += correct. Good.

Wall restitution repeated iterations: after first vn positive skip, okay. Contact counts max 4 per actual contacts, fine.

Potential penetration non-persistent. At 15 sec balls not overlapping. Good.

Should reset wall orientation exact at 0 draw yes. Running before screenshot elapsed 0.

Perhaps fix angular physics.

Perhaps test after fix motion and pause reset.

Perhaps sample 1 sec collisions and 10 sec. Browser motion costs apparently advances several seconds.

Looks good. Potential balls near corner perhaps one outside? At screenshot 6.91 ball 9 at bottom vertex touches, contained. Should pause/reset after correction.

Should verify pause freeze perhaps inspect after delay via inspect? Browser inspect immediate perhaps enough; motion while paused should same and takes sec. Could motion paused; it may no changes. But enough. Reset.

Good. Should respond concise report checked and unverified per instructions. Mention index, fixed step, controls. Remaining unverified perhaps extended multi-minute/mobile not extensively tested. No need more tools. Ensure file exists yes.

Could one issue ball ball wall collision uses wallAngle integration modulo and get vertices. Rotation exact period 5. Good.

Respond with checks.