From d644eff20a20809dffbb098b2e74dbd4c1ef5fb9 Mon Sep 17 00:00:00 2001
From: Matthew Kosarek <mattkae@protonmail.com>
Date: Sun, 11 Apr 2021 16:35:25 -0400
Subject: Nearly have good pill-lin collisions working, just need to get the
actual equation right
---
frontend/2d/_collisions/pill_line.html | 18 +++-
frontend/2d/_collisions/pill_line.html.content | 15 ++++
frontend/2d/_collisions/pill_line/dist/output.wasm | Bin 57400 -> 60622 bytes
frontend/2d/_collisions/pill_line/main.cpp | 98 ++++++++++++++++++---
4 files changed, 115 insertions(+), 16 deletions(-)
(limited to 'frontend')
diff --git a/frontend/2d/_collisions/pill_line.html b/frontend/2d/_collisions/pill_line.html
index 4cbefde..8b3539a 100644
--- a/frontend/2d/_collisions/pill_line.html
+++ b/frontend/2d/_collisions/pill_line.html
@@ -47,6 +47,21 @@
</ul>
</nav>
<script src="./pill_line/dist/output.js"></script>
+ <script>
+ window.onload = function() {
+ var lPlayElement = document.getElementById('gl_canvas_play'),
+ lStopElement = document.getElementById('gl_canvas_stop');
+ lPlayElement.addEventListener('click', function() {
+ lPlayElement.style.display = 'none';
+ lStopElement.style.display = 'block';
+ });
+ lStopElement.addEventListener('click', function() {
+ lStopElement.style.display = 'none';
+ lPlayElement.style.display = 'block';
+ });
+ }
+
+ </script>
<section>
<h1>Pill-Line</h1>
<article>
@@ -72,7 +87,6 @@
</footer>
</article>
</section>
- <li>
- </main>
+don </main>
</body>
</html>
diff --git a/frontend/2d/_collisions/pill_line.html.content b/frontend/2d/_collisions/pill_line.html.content
index fb2994c..c534d93 100644
--- a/frontend/2d/_collisions/pill_line.html.content
+++ b/frontend/2d/_collisions/pill_line.html.content
@@ -1,4 +1,19 @@
<script src="./pill_line/dist/output.js"></script>
+ <script>
+ window.onload = function() {
+ var lPlayElement = document.getElementById('gl_canvas_play'),
+ lStopElement = document.getElementById('gl_canvas_stop');
+ lPlayElement.addEventListener('click', function() {
+ lPlayElement.style.display = 'none';
+ lStopElement.style.display = 'block';
+ });
+ lStopElement.addEventListener('click', function() {
+ lStopElement.style.display = 'none';
+ lPlayElement.style.display = 'block';
+ });
+ }
+
+ </script>
<section>
<h1>Pill-Line</h1>
<article>
diff --git a/frontend/2d/_collisions/pill_line/dist/output.wasm b/frontend/2d/_collisions/pill_line/dist/output.wasm
index 3b6a673..c671a7e 100755
Binary files a/frontend/2d/_collisions/pill_line/dist/output.wasm and b/frontend/2d/_collisions/pill_line/dist/output.wasm differ
diff --git a/frontend/2d/_collisions/pill_line/main.cpp b/frontend/2d/_collisions/pill_line/main.cpp
index 76dc7d4..0476b98 100644
--- a/frontend/2d/_collisions/pill_line/main.cpp
+++ b/frontend/2d/_collisions/pill_line/main.cpp
@@ -19,6 +19,8 @@ struct Rigidbody {
float32 rotationalVelocity = 0.f;
float32 rotation = 0.f;
float32 mass = 1.f;
+ float32 cofOfRestition = 0.7f;
+ float32 momentOfInertia = 0.f;
void reset() {
force = { 0, 0 };
@@ -41,6 +43,10 @@ struct Rigidbody {
rotation += (rotationalVelocity * deltaTimeSeconds);
}
+
+ void setMomentOfInertia(float32 moi) {
+ momentOfInertia = moi;
+ }
};
struct Pill {
@@ -95,6 +101,9 @@ struct Pill {
shape.load(vertices, numVertices, renderer);
body.reset();
+ // https://byjus.com/jee/moment-of-inertia-of-ellipse/
+ body.momentOfInertia = (body.mass * (a * a + b * b)) / 4.f;
+
a = width / 2.f;
b = height / 2.f;
@@ -121,20 +130,30 @@ struct Pill {
struct LineSegment {
OrthographicShape shape;
+ Rigidbody body;
Vector2 start;
Vector2 end;
+ float32 length;
Vector2 normal;
OrthographicVertex vertices[2];
void load(OrthographicRenderer* renderer, Vector4 color, Vector2 inStart, Vector2 inEnd) {
start = inStart;
end = inEnd;
+ length = (start - end).length();
vertices[0].position = start;
vertices[0].color = color;
vertices[1].position = end;
vertices[1].color = color;
normal = (end - start).getPerp().normalize();
shape.load(vertices, 2, renderer);
+
+ body.reset();
+ body.mass = 100000.f;
+ body.cofOfRestition = 1.f;
+ body.rotationalVelocity = 0;
+ body.velocity = Vector2();
+ body.momentOfInertia = body.mass * (length / 2.f);
}
void render(OrthographicRenderer* renderer) {
@@ -159,9 +178,10 @@ struct LineSegment {
struct IntersectionResult {
bool intersect = false;
- Vector2 pointOfIntersection;
Vector2 collisionNormal;
Vector2 relativeVelocity;
+ Vector2 firstPointOfApplication;
+ Vector2 secondPointOfApplication;
};
EM_BOOL onPlayClicked(int eventType, const EmscriptenMouseEvent* mouseEvent, void* userData);
@@ -209,6 +229,34 @@ float32 areaOfTriangle(Vector2 a, Vector2 b, Vector2 c) {
IntersectionResult getIntersection(Pill* pill, LineSegment* segment) {
IntersectionResult result;
+
+ /**
+
+ Formula for finding equation of pill:
+ 1) Using the parametrized equation of a line:
+ x(t) = x1 + (x2 - x1) * t
+ y(t) = y1 + (y2 - y1) * t
+ 2) Knowing the equation of a translated and rotated ellipse:
+
+ Define x and y as follows:
+
+ x = x_1 + l, where l is the translation in x
+ y = y_1 + h, where h is the translation in y
+
+ Therefore, the general equation of a rotated ellipse is:
+
+ (x * cos(theta) + y * sin(theta)) / (a * a)
+ + (y * cos(theta) - x * sin(theta)) / b * b = 1
+
+ ( + l + x * cos(theta) + y * sin(theta)) / (a * a)
+ + (y + h + y * cos(theta) + y * sin(theta)) / (a * a)
+
+ 3) Plug in the parametrized equation of our line for x_1 and y_2.
+
+ 4) If the determinant >= 0, we have an intersection, otherwise, nothing.
+
+ **/
+
/*float32 rotationAngleOfPill = pill->body.rotation;
Vector2 translationOfPill = pill->body.position;
@@ -249,20 +297,37 @@ IntersectionResult getIntersection(Pill* pill, LineSegment* segment) {
float32 t1 = -B + determinant / (2 * A);
float32 t2 = -B - determinant / (2 * A);
- Vector2 pointAtT1 = { segment->start.x + (t1 * (segment->end.x - segment->start.x)), segment->start.y + (t1 * (segment->end.y - segment->start.y)) };
+ Vector2 pointAtT1 = pill->shape.model * Vector2 { segment->start.x + (t1 * (segment->end.x - segment->start.x)), segment->start.y + (t1 * (segment->end.y - segment->start.y)) };
Vector2 pointAtT2 = { segment->start.x + (t2 * (segment->end.x - segment->start.x)), segment->start.y + (t2 * (segment->end.y - segment->start.y)) };
- printf("Intersecting\n");
result.intersect = true;
- result.pointOfIntersection = pointAtT1 - pill->body.position;;
- result.relativeVelocity = Vector2() - pill->body.velocity;
+ result.relativeVelocity = pill->body.velocity - segment->body.velocity;;
result.collisionNormal = (pointAtT1 - pill->body.position).normalize();
+ result.firstPointOfApplication = pointAtT1 - pill->body.position;
+ result.secondPointOfApplication = pointAtT1 - ((segment->end - segment->start) / 2.f);
return result;
}
void resolveCollision(Rigidbody* first, Rigidbody* second, IntersectionResult* ir) {
-
+ Vector2 relativeVelocity = ir->relativeVelocity;
+ Vector2 collisionNormal = ir->collisionNormal;
+ Vector2 firstPerp = ir->firstPointOfApplication.getPerp();
+ Vector2 secondPerp = ir->secondPointOfApplication.getPerp();
+
+ float32 cofOfRestition = (first->cofOfRestition + second->cofOfRestition) / 2.f;
+ float32 lNumerator = (relativeVelocity * -(1.0 + cofOfRestition)).dot(collisionNormal);
+ float32 lLinearDenomPart = collisionNormal.dot(collisionNormal * (1 / first->mass + 1 / second->mass));
+ float32 lRotationalDenomPart = powf(firstPerp.dot(collisionNormal), 2) / first->momentOfInertia
+ + powf(secondPerp.dot(collisionNormal), 2) / second->momentOfInertia;
+
+ float32 lImpulseMagnitude = lNumerator / (lLinearDenomPart);// + lRotationalDenomPart);
+
+ first->velocity = first->velocity + (collisionNormal * (lImpulseMagnitude / first->mass));
+ second->velocity = second->velocity - (collisionNormal * (lImpulseMagnitude / second->mass));
+
+ //first->rotationalVelocity = first->rotationalVelocity + firstPerp.dot(collisionNormal * lImpulseMagnitude) / first->momentOfInertia;
+ //second->rotationalVelocity = second->rotationalVelocity - secondPerp.dot(collisionNormal * lImpulseMagnitude) / second->momentOfInertia;
}
void update(float32 deltaTimeSeconds, void* userData) {
@@ -280,20 +345,25 @@ void update(float32 deltaTimeSeconds, void* userData) {
if (ir.intersect) {
// Find the exact moment that the intersection happens by rewinding the simulation until we're not intersecting
- while (ir.intersect) {
- pill = copyPill.copy();
- deltaTimeSeconds /= 2.f;
- pill.update(deltaTimeSeconds);
+ IntersectionResult subIr = ir;
+ float32 subdividedTimeSeconds = deltaTimeSeconds;
+ do {
+ ir = subIr;
- ir = getIntersection(&pill, &segmentList[lineIdx]);
+ pill = copyPill.copy();
+ subdividedTimeSeconds /= 2.f;
+ pill.update(subdividedTimeSeconds);
- if (deltaTimeSeconds <= 0.f) {
+ subIr = getIntersection(&pill, &segmentList[lineIdx]);
+ if (subdividedTimeSeconds == 0.f) {
printf("Error: Should not be happening.\n");
break;
}
- }
+ } while (subIr.intersect);
- printf("Found intersection at timestamp: %f\n", deltaTimeSeconds);
+ printf("Found intersection at timestamp: %f\n", subdividedTimeSeconds);
+ resolveCollision(&pill.body, &segmentList[lineIdx].body, &ir);
+ pill.update(deltaTimeSeconds - subdividedTimeSeconds);
}
}
--
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