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authorMatthew Kosarek <mattkae@protonmail.com>2021-10-19 07:10:49 -0400
committerMatthew Kosarek <mattkae@protonmail.com>2021-10-19 07:10:49 -0400
commita003378e602107d421b819ac629493b5c6444762 (patch)
tree6c15bdd83cf18780cbb581c57ff3b765b3f17299 /3d
parentc025960c6fbeac17d94a14d14cd13b42737bc80e (diff)
Working sphere sphere intersection
Diffstat (limited to '3d')
-rwxr-xr-x3d/rigidbody/dist/output.wasmbin56137 -> 62008 bytes
-rw-r--r--3d/rigidbody/main.cpp117
2 files changed, 108 insertions, 9 deletions
diff --git a/3d/rigidbody/dist/output.wasm b/3d/rigidbody/dist/output.wasm
index 3702497..1bc13cc 100755
--- a/3d/rigidbody/dist/output.wasm
+++ b/3d/rigidbody/dist/output.wasm
Binary files differ
diff --git a/3d/rigidbody/main.cpp b/3d/rigidbody/main.cpp
index bf6af58..f95e634 100644
--- a/3d/rigidbody/main.cpp
+++ b/3d/rigidbody/main.cpp
@@ -13,6 +13,7 @@
#include <cmath>
#include <cfloat>
+// -- Rigidbody updates
struct Impulse {
Vector3 force = { 0, 0, 0 };
Vector3 pointOfApplication = { 0, 0, 0 };
@@ -33,6 +34,7 @@ struct Rigidbody3d {
Vector3 rotationalVelocity;
Quaternion rotation;
float32 momentOfInertia = 1.f;
+ float32 cofOfRestitution = 1.f;
void reset() {
numImpulses = 0;
@@ -100,14 +102,16 @@ struct Rigidbody3d {
}
};
+// -- Sphere definition
float32 bounds = 20.f;
struct Sphere {
Mesh3d mesh;
+ Rigidbody3d previousBody;
Rigidbody3d body;
+ float32 radius = 5.f;
void load(Renderer3d* renderer) {
- const float32 scale = 3.f;
const float32 angleIncrements = 2.f;
const int32 numFaces = static_cast<int32>((180.f / angleIncrements + 1) * (360.f / angleIncrements + 1));
const int32 numVertices = 4.f * numFaces;
@@ -135,22 +139,22 @@ struct Sphere {
const auto nextCosTheta = cos(DEG_TO_RAD(theta + angleIncrements));
// Top Left Point
- auto topLeftPoint = Vector3(scale * sinPhi * cosTheta, scale * sinPhi * sinTheta, scale * cosPhi);
+ auto topLeftPoint = Vector3(radius * sinPhi * cosTheta, radius * sinPhi * sinTheta, radius * cosPhi);
auto topLeftIdx = index++;
vertices[vidx++] = { topLeftPoint, topLeftPoint.normalize(), color };
// Bottom Left Point
- auto bottomLeftPoint = Vector3(scale * nextSinPhi * cosTheta, scale * nextSinPhi * sinTheta, scale * nextCosPhi);
+ auto bottomLeftPoint = Vector3(radius * nextSinPhi * cosTheta, radius * nextSinPhi * sinTheta, radius * nextCosPhi);
auto bottomLeftIdx = index++;
vertices[vidx++] = { bottomLeftPoint, bottomLeftPoint.normalize(), color };
// Bottom Right Point
- auto bottomRightPoint = Vector3(scale * nextSinPhi * nextCosTheta, scale * nextSinPhi * nextSinTheta, scale * nextCosPhi);
+ auto bottomRightPoint = Vector3(radius * nextSinPhi * nextCosTheta, radius * nextSinPhi * nextSinTheta, radius * nextCosPhi);
auto bottomRightIdx = index++;
vertices[vidx++] = { bottomRightPoint, bottomRightPoint.normalize(), color };
// Top Right Point
- auto topRightPoint = Vector3(scale * sinPhi * nextCosTheta, scale * sinPhi * nextSinTheta, scale * cosPhi);
+ auto topRightPoint = Vector3(radius * sinPhi * nextCosTheta, radius * sinPhi * nextSinTheta, radius * cosPhi);
auto topRightIdx = index++;
vertices[vidx++] = { topRightPoint, topRightPoint.normalize(), color };
@@ -168,7 +172,7 @@ struct Sphere {
body.position = Vector3 { 0.f, 0.f, 0.f };
body.velocity = Vector3 { 0.f, 0.f, 0.f };
- float32 singleFaceArea = scale;
+ float32 singleFaceArea = radius;
body.momentOfInertia = (body.mass * singleFaceArea) / 6.f;
delete [] vertices;
@@ -176,8 +180,10 @@ struct Sphere {
}
void update(float32 dtSeconds) {
+ previousBody = body;
body.update(dtSeconds);
+ // -- Constrain inside of the box
if (body.position.x > bounds) {
body.position.x = bounds;
body.velocity.x = -body.velocity.x;
@@ -218,11 +224,23 @@ struct Sphere {
}
};
+// -- Intersection info
+struct IntersectionResult {
+ bool intersect = false;
+ Vector3 collisionNormal;
+ Vector3 relativeVelocity;
+ Vector3 firstPointOfApplication;
+ Vector3 secondPointOfApplication;
+};
+
+
EM_BOOL onPlayClicked(int eventType, const EmscriptenMouseEvent* mouseEvent, void* userData);
EM_BOOL onStopClicked(int eventType, const EmscriptenMouseEvent* mouseEvent, void* userData);
EM_BOOL onForceApplicationRequested(int eventType, const EmscriptenMouseEvent* mouseEvent, void* userData);
void load();
+IntersectionResult getIntersection(Sphere* first, Sphere* second);
+void resolveIntersection(Rigidbody3d* first, Rigidbody3d* second, IntersectionResult* ir);
void update(float32 time, void* userData);
void unload();
@@ -255,20 +273,101 @@ void load() {
sphereList[1].load(&renderer);
sphereList[1].body.mass = 6.f;
sphereList[1].body.position = Vector3(-10.f, 0, 5);
- sphereList[1].body.velocity = Vector3(10.f, 10.f, -10.f);
+ sphereList[1].body.velocity = Vector3(10.f, -10.f, -10.f);
sphereList[1].body.rotationalVelocity = Vector3(1.f, 1.f, 1.f);
camera.projection = Mat4x4().getPerspectiveProjection(0.1f, 10000.f, DEG_TO_RAD(45.f), 800.f / 600.f);
- camera.view = Mat4x4().translate({ 0, 0, -40.f });
+ camera.view = Mat4x4().translate({ 0, 0, -60.f });
mainLoop.run(update);
}
+IntersectionResult getIntersection(Sphere* first, Sphere* second) {
+ IntersectionResult ir;
+ auto distance = (first->body.position - second->body.position).length();
+ if (distance <= first->radius + second->radius) {
+ ir.intersect = true;
+ }
+ else {
+ ir.intersect = false;
+ return ir;
+ }
+
+ auto positionDiff = first->body.position - second->body.position;
+ auto positionDirection = positionDiff.normalize();
+ ir.relativeVelocity = first->body.velocity - second->body.velocity;
+ ir.firstPointOfApplication = positionDirection * first->radius;
+ ir.secondPointOfApplication = positionDirection * second->radius;
+ ir.collisionNormal = (positionDirection + ir.relativeVelocity.negate().normalize()).normalize();
+
+ return ir;
+}
+
+void resolveIntersection(Rigidbody3d* first, Rigidbody3d* second, IntersectionResult* ir) {
+ Vector3 relativeVelocity = ir->relativeVelocity;
+ Vector3 collisionNormal = ir->collisionNormal;
+ Vector3 firstPerp = ir->firstPointOfApplication.cross(relativeVelocity);
+ Vector3 secondPerp = ir->secondPointOfApplication.cross(relativeVelocity);
+ float32 firstPerpNorm = firstPerp.dot(collisionNormal);
+ float32 sndPerpNorm = secondPerp.dot(collisionNormal);
+
+ float32 cofOfRestitution = (first->cofOfRestitution + second->cofOfRestitution) / 2.f;
+ float32 numerator = (relativeVelocity * (-1 * (1.f + cofOfRestitution))).dot(collisionNormal);
+ float32 linearDenomPart = collisionNormal.dot(collisionNormal * (1.f / first->mass + 1.f / second->mass));
+ float32 rotationalDenomPart = (firstPerpNorm * firstPerpNorm) / first->momentOfInertia + (sndPerpNorm * sndPerpNorm) / second->momentOfInertia;
+
+ float32 impulseMagnitude = numerator / (linearDenomPart + rotationalDenomPart);
+ first->velocity = first->velocity + (collisionNormal * (impulseMagnitude / first->mass));
+ second->velocity = second->velocity - (collisionNormal * (impulseMagnitude / second->mass));
+
+ first->rotationalVelocity = first->rotationalVelocity + firstPerp.dot(collisionNormal * impulseMagnitude) / first->momentOfInertia;
+ second->rotationalVelocity = second->rotationalVelocity - secondPerp.dot(collisionNormal * impulseMagnitude) / second->momentOfInertia;
+
+}
+
void update(float32 deltaTimeSeconds, void* userData) {
+ // -- Update
for (int32 idx = 0; idx < numSpheres; idx++) {
sphereList[idx].update(deltaTimeSeconds);
}
- // Renderer
+ // -- Check collisions
+ for (int32 idx = 0; idx < numSpheres; idx++) {
+ auto first = &sphereList[idx];
+ for (int32 otherIdx = idx + 1; otherIdx < numSpheres; otherIdx++) {
+ auto second = &sphereList[otherIdx];
+
+ auto ir = getIntersection(first, second);
+ if (!ir.intersect) { continue; }
+
+ // Find out where the intersection took place. We will rewind the simulation
+ // until the spheres are no longer intersecting.
+ const float32 numDtSubdivision = 8.f;
+ const float32 subdivisionSeconds = deltaTimeSeconds / numDtSubdivision;
+ int32 currentDtSubdivision = 1.f;
+ IntersectionResult tempIr = ir;
+ do {
+ ir = tempIr;
+
+ // Restore the bodies to the point before the collision happened
+ first->body = first->previousBody;
+ second->body = second->previousBody;
+
+ // Subdivide the timestep to get a more granular intersection result
+ float32 currentUpdateStep = deltaTimeSeconds - (currentDtSubdivision * subdivisionSeconds);
+
+ first->update(currentUpdateStep);
+ second->update(currentUpdateStep);
+
+ tempIr = getIntersection(first, second);
+ currentDtSubdivision++;
+ } while (tempIr.intersect);
+
+ // Exact intersection point is found. Now we can solve it
+ resolveIntersection(&first->body, &second->body, &ir);
+ }
+ }
+
+ // -- Render
renderer.render(&camera);
for (int32 idx = 0; idx < numSpheres; idx++) {
sphereList[idx].render(&renderer);