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-rw-r--r--2d/softbody/softbody_1/damped.cpp148
-rwxr-xr-x2d/softbody/softbody_1/dist/output.wasmbin69604 -> 58758 bytes
2 files changed, 27 insertions, 121 deletions
diff --git a/2d/softbody/softbody_1/damped.cpp b/2d/softbody/softbody_1/damped.cpp
index f56f346..0525e25 100644
--- a/2d/softbody/softbody_1/damped.cpp
+++ b/2d/softbody/softbody_1/damped.cpp
@@ -25,13 +25,6 @@ namespace Damped {
void unload();
};
- enum DampedSpringType {
- None = 0,
- Overdamped = 1,
- Underdamped = 2,
- Critical = 3
- };
-
struct DampedSpring {
DampedSpringWeight* weight;
@@ -42,24 +35,14 @@ namespace Damped {
int32 numVertices = 0;
// Initialization variables
- float32 initialDisplacement = 0.f;
float32 k = 4; // DampedSpring Constant, in N / m (Hooke's Law)
float32 c = 1.f; // Viscous damping coefficient (Damping force)
- // Discovered during initialization
- DampedSpringType type = DampedSpringType::None;
- float32 R = 2.f;
- float32 gamma = 6.2;
- float32 discriminant = 0.f;
- float32 omega1 = 0.f;
- float32 c1 = 0.f;
- float32 c2 = 0.f;
- float32 r1 = 0.f;
- float32 r2 = 0.f;
-
// Update variables
- float32 displacement = 0.f;
- float32 timeElapsed = 0.f;
+ float32 force = 0.f;
+ float32 acceleration = 0.f;
+ float32 velocity = 0.f;
+ float32 position = 0.f;
void load(Renderer2d* renderer, DampedSpringWeight* inWieight, float32 length, float32 loopRadius, float32 initialDisplacement, float32 inK, float32 inC);
@@ -122,7 +105,8 @@ namespace Damped {
void DampedSpringWeight::load(Renderer2d* renderer, float32 inMass, Vector4 startColor, Vector4 endColor) {
mass = inMass;
- radius = mass * 16.f;
+ radius = mass * 8.f;
+ if (radius > 42.f) radius = 42.f;
const int32 numSegments = 96;
const float32 radiansPerSegment = (2.f * PI) / static_cast<float>(numSegments);
const int32 numVertices = numSegments * 3;
@@ -168,8 +152,7 @@ namespace Damped {
const float32 epsilon = 0.0001f;
- void DampedSpring::load(Renderer2d* renderer, DampedSpringWeight* inWeight, float32 length, float32 loopRadius, float32 inInitialDisplacement, float32 inK, float32 inC) {
- initialDisplacement = inInitialDisplacement;
+ void DampedSpring::load(Renderer2d* renderer, DampedSpringWeight* inWeight, float32 length, float32 loopRadius, float32 initialDisplacement, float32 inK, float32 inC) {
weight = inWeight;
k = inK;
c = inC;
@@ -179,92 +162,22 @@ namespace Damped {
float32 B = c;
float32 C = k;
-
- discriminant = B * B - (4 * A * C);
- timeElapsed = 0;
- displacement = 0;
+ float32 discriminant = B * B - (4 * A * C);
+ acceleration = 0;
+ velocity = 0;
+ position = initialDisplacement;
if (discriminant < epsilon && discriminant > -epsilon) {
// Real repeated root (~ zero): Critically damped motion
printf("Critically damped motion.\n");
-
- type = DampedSpringType::Critical;
-
- r1 = -B / (2 * A);
- r2 = r1;
-
- // Solve for the initial displacement.
- c2 = (initialDisplacement - r1) / (r2);
- c2 = r2 * c2;
- c1 = r1;
- printf("Equation: %f e^(%f t) + %f t e^(%f t)\n", c1, r1, c2, r2);
}
else if (discriminant > 0) {
// Two real roots (greater than zero): Overdamped motion
printf("Overdamped motion.\n");
-
- type = DampedSpringType::Overdamped;
-
- // Discover the two treal roots. Both of these WILL be negative.
- float32 sqrtDis = sqrtf(discriminant);
- r1 = (-B + sqrtDis) / (2 * A);
- r2 = (-B - sqrtDis) / (2 * A);
-
- // Now, solve for c1 and c2 given the initial displacement. The equation is:
- // x(0) = r1 * c1 * e^(r1 * t) + r2 * c2 * e^(r2 * t) ->
- // x(0) = r1 * c1 + r2 * c2 ->
- // initialDisplacement = r1 * c1 + r2 * c2; -> if abs(r1) > abs(r2) => c1 = 1, else c2 = 1
- if (r1 < r2) {
- c2 = (initialDisplacement - r1) / (r2);
- c2 = r2 * c2;
- c1 = r1;
- }
- else {
- c1 = (initialDisplacement - r2) / (r1);
- c1 = r1 * c1;
- c2 = r2;
- }
-
- printf("Equation: %f e^(%f t) + %f e^(%f t)\n", c1, r1, c2, r2);
}
else {
// Complex pair (less than zero): Underdamped motion
printf("Underdamped motion.\n");
-
- type = DampedSpringType::Underdamped;
- float32 sqrtDis = sqrtf(-discriminant);
- omega1 = sqrtf(sqrtDis) / (2.f * A); // Note that we negate the discriminant to get the REAL positive part.
-
- r1 = (-B + sqrtDis) / (2 * A);
- r2 = (-B - sqrtDis) / (2 * A);
-
- // Now, solve for c1 and c2 given the initial displacement. The equation is:
- // x(0) = r1 * c1 * e^(r1 * t) + r2 * c2 * e^(r2 * t) ->
- // x(0) = r1 * c1 + r2 * c2 ->
- // initialDisplacement = r1 * c1 + r2 * c2; -> if abs(r1) > abs(r2) => c1 = 1, else c2 = 1
- if (r1 < r2) {
- c2 = (initialDisplacement - r1) / (r2);
- c2 = r2 * c2;
- c1 = r1;
- }
- else {
- c1 = (initialDisplacement - r2) / (r1);
- c1 = r1 * c1;
- c2 = r2;
- }
-
- // At this point, we have:
- // x(t) = c1 cos(omega1 t) + c2 cos(omega1 t) ->
- // x(t) = A cos(omega1 t - Φ) ->
- // Now we need to solve for A and Φ for our initial displacement, so:
- // initialDisplacement = c1
- R = sqrtf(c1 * c1 + c2 * c2);
- if (initialDisplacement < 0) {
- R = -R;
- }
- gamma = atanf(c2 / c1);
-
- printf("Equation: %f e^(-(%f / %f) t) * cos(%f t - %f)\n", R, c, weight->mass, omega1, gamma);
}
const int32 verticesPerSegment = 6;
@@ -279,13 +192,20 @@ namespace Damped {
const float32 offset = 0.25f;
int32 vidx = 0;
+ float32 dx = position;
for (int pidx = 0; pidx < numSegments; pidx++) {
float32 y1 = lengthIncrement * pidx;
float32 x1 = loopWidth * sinf(frequency * y1 + offset);
float32 y2 = y1 + lengthIncrement;
float32 x2 = loopWidth * sinf(frequency * y2 + offset);
-
+
+ float32 y1Offset = dx * (1.f - pidx / static_cast<float32>(numSegments));
+ float32 y2Offset = dx * (1.f - (pidx + 1) / static_cast<float32>(numSegments));
+
+ y1 += y1Offset;
+ y2 += y2Offset;
+
vertices[vidx++].position = Vector2(x1, y1);
vertices[vidx++].position = Vector2(x1, y2);
vertices[vidx++].position = Vector2(x2, y1);
@@ -297,31 +217,17 @@ namespace Damped {
shape.load(vertices, numVertices, renderer, GL_DYNAMIC_DRAW);
shape.model = Mat4x4().translateByVec2(Vector2(400, 300));
- weight->shape.model = shape.model.translateByVec2(Vector2(0, -weight->radius));
+ weight->shape.model = shape.model.translateByVec2(Vector2(0, -weight->radius + dx));
}
void DampedSpring::update(float32 dtSeconds) {
- timeElapsed += dtSeconds;
-
- float32 lastDisplacement = displacement;
-
- switch (type) {
- case DampedSpringType::Critical:
- displacement = c1 * pow(E, r1 * timeElapsed) + c2 * timeElapsed * pow(E, r2 * timeElapsed);
- break;
- case DampedSpringType::Overdamped:
- displacement = c1 * pow(E, r1 * timeElapsed) + c2 * pow(E, r2 * timeElapsed);
- break;
- case DampedSpringType::Underdamped: {
- float32 exponent = -(c / (2 * weight->mass)) * timeElapsed;
- displacement = R * pow(E, exponent) * (cosf(omega1 * timeElapsed - gamma));
- break;
- }
- default:
- break;
- }
-
- float32 dx = displacement - lastDisplacement;
+ force = -weight->mass * acceleration - c * velocity - k * position;
+ acceleration = (force * dtSeconds) / weight->mass;
+ velocity = velocity + acceleration * dtSeconds;
+ float32 lastPosition = position;
+ position = position + velocity * dtSeconds;
+
+ float32 dx = position - lastPosition;
int32 vidx = 0;
for (int pidx = 0; pidx < numSegments; pidx++) {
float32 y1Offset = dx * (1.f - pidx / static_cast<float32>(numSegments));
diff --git a/2d/softbody/softbody_1/dist/output.wasm b/2d/softbody/softbody_1/dist/output.wasm
index b034adc..8f7c621 100755
--- a/2d/softbody/softbody_1/dist/output.wasm
+++ b/2d/softbody/softbody_1/dist/output.wasm
Binary files differ
generated by cgit v1.2.1 (git 2.18.0) at 2024-10-18 15:30:58 +0000