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-rw-r--r--2d/softbody/softbody_1.html18
-rw-r--r--2d/softbody/softbody_1.html.content18
-rw-r--r--2d/softbody/softbody_1/damped.cpp136
-rw-r--r--2d/softbody/softbody_1/damped.h1
-rw-r--r--2d/softbody/softbody_1/dist/output.js3
-rwxr-xr-x2d/softbody/softbody_1/dist/output.wasmbin65388 -> 69005 bytes
-rw-r--r--2d/softbody/softbody_1/main.cpp6
7 files changed, 148 insertions, 34 deletions
diff --git a/2d/softbody/softbody_1.html b/2d/softbody/softbody_1.html
index 3f0fc40..ae4b743 100644
--- a/2d/softbody/softbody_1.html
+++ b/2d/softbody/softbody_1.html
@@ -86,6 +86,7 @@
document.getElementById('damped_spring_length'),
document.getElementById('damped_start_position'),
document.getElementById('damped_spring_constant'),
+ document.getElementById('damped_viscous_constant'),
document.getElementById('damped_spring_mass')
]);
@@ -118,6 +119,7 @@
Damped_SetDisplacement = Module.cwrap('Damped_SetDisplacement', 'void', ['number']),
Damped_SetK = Module.cwrap('Damped_SetK', 'void', ['number']),
Damped_SetMass = Module.cwrap('Damped_SetMass', 'void', ['number']),
+ Damped_SetC = Module.cwrap('Damped_SetC', 'void', ['number']),
Undamped_lengthSlider = document.getElementById('undamped_spring_length'),
Undamped_displacementSlider = document.getElementById('undamped_start_position'),
@@ -128,6 +130,7 @@
Damped_displacementSlider = document.getElementById('damped_start_position'),
Damped_kSlider = document.getElementById('damped_spring_constant'),
Damped_massSlider = document.getElementById('damped_spring_mass'),
+ Damped_cSlider = document.getElementById('damped_viscous_constant'),
undampedSetLength = function(value) {
value = Number(value);
@@ -171,6 +174,7 @@
Damped_displacementSlider.addEventListener('change', function(event) { Damped_SetDisplacement(Number(event.target.value)); });
Damped_kSlider.addEventListener('change', function(event) { Damped_SetK(Number(event.target.value)); });
Damped_massSlider.addEventListener('change', function(event) { Damped_SetMass(Number(event.target.value)); });
+ Damped_cSlider.addEventListener('change', function(event) { Damped_SetC(Number(event.target.value)); });
};
}
@@ -234,25 +238,31 @@
</h2>
<p>
<span class='widget_container'>
- <label for='undamped_spring_length'>Spring Length (m)</label>
+ <label for='damped_spring_length'>Spring Length (m)</label>
<input type='range' id='damped_spring_length' min="50" max="300" value="150"/>
<span></span>
</span>
<span class='widget_container'>
- <label for='undamped_start_position'>Start Displacement (m)</label>
+ <label for='damped_start_position'>Start Displacement (m)</label>
<input type='range' id='damped_start_position' min='-150' max='150' value='0'/>
<span></span>
</span>
<span class='widget_container'>
- <label for='undamped_spring_constant'>Spring Constant (N / m)</label>
+ <label for='damped_spring_constant'>Spring Constant (N / m)</label>
<input type='range' id='damped_spring_constant' min='0.1' max='20.0' value='1.0' step='0.1'/>
<span></span>
</span>
+ <span class='widget_container'>
+ <label for='damped_viscous_constant'>Viscous Damping Constant (N / m)</label>
+ <input type='range' id='damped_viscous_constant' min='0.1' max='50.0' value='1.0' step='0.1'/>
+ <span></span>
+ </span>
+
<span class='widget_container'>
- <label for='undamped_spring_mass'>Mass (kg)</label>
+ <label for='damped_spring_mass'>Mass (kg)</label>
<input type='range' id='damped_spring_mass' min='0.1' max='10.0' value='1.0' step='0.1'/>
<span></span>
</span>
diff --git a/2d/softbody/softbody_1.html.content b/2d/softbody/softbody_1.html.content
index bef14d8..c5fb3cc 100644
--- a/2d/softbody/softbody_1.html.content
+++ b/2d/softbody/softbody_1.html.content
@@ -33,6 +33,7 @@
document.getElementById('damped_spring_length'),
document.getElementById('damped_start_position'),
document.getElementById('damped_spring_constant'),
+ document.getElementById('damped_viscous_constant'),
document.getElementById('damped_spring_mass')
]);
@@ -65,6 +66,7 @@
Damped_SetDisplacement = Module.cwrap('Damped_SetDisplacement', 'void', ['number']),
Damped_SetK = Module.cwrap('Damped_SetK', 'void', ['number']),
Damped_SetMass = Module.cwrap('Damped_SetMass', 'void', ['number']),
+ Damped_SetC = Module.cwrap('Damped_SetC', 'void', ['number']),
Undamped_lengthSlider = document.getElementById('undamped_spring_length'),
Undamped_displacementSlider = document.getElementById('undamped_start_position'),
@@ -75,6 +77,7 @@
Damped_displacementSlider = document.getElementById('damped_start_position'),
Damped_kSlider = document.getElementById('damped_spring_constant'),
Damped_massSlider = document.getElementById('damped_spring_mass'),
+ Damped_cSlider = document.getElementById('damped_viscous_constant'),
undampedSetLength = function(value) {
value = Number(value);
@@ -118,6 +121,7 @@
Damped_displacementSlider.addEventListener('change', function(event) { Damped_SetDisplacement(Number(event.target.value)); });
Damped_kSlider.addEventListener('change', function(event) { Damped_SetK(Number(event.target.value)); });
Damped_massSlider.addEventListener('change', function(event) { Damped_SetMass(Number(event.target.value)); });
+ Damped_cSlider.addEventListener('change', function(event) { Damped_SetC(Number(event.target.value)); });
};
}
@@ -181,25 +185,31 @@
</h2>
<p>
<span class='widget_container'>
- <label for='undamped_spring_length'>Spring Length (m)</label>
+ <label for='damped_spring_length'>Spring Length (m)</label>
<input type='range' id='damped_spring_length' min="50" max="300" value="150"/>
<span></span>
</span>
<span class='widget_container'>
- <label for='undamped_start_position'>Start Displacement (m)</label>
+ <label for='damped_start_position'>Start Displacement (m)</label>
<input type='range' id='damped_start_position' min='-150' max='150' value='0'/>
<span></span>
</span>
<span class='widget_container'>
- <label for='undamped_spring_constant'>Spring Constant (N / m)</label>
+ <label for='damped_spring_constant'>Spring Constant (N / m)</label>
<input type='range' id='damped_spring_constant' min='0.1' max='20.0' value='1.0' step='0.1'/>
<span></span>
</span>
+ <span class='widget_container'>
+ <label for='damped_viscous_constant'>Viscous Damping Constant (N / m)</label>
+ <input type='range' id='damped_viscous_constant' min='0.1' max='50.0' value='1.0' step='0.1'/>
+ <span></span>
+ </span>
+
<span class='widget_container'>
- <label for='undamped_spring_mass'>Mass (kg)</label>
+ <label for='damped_spring_mass'>Mass (kg)</label>
<input type='range' id='damped_spring_mass' min='0.1' max='10.0' value='1.0' step='0.1'/>
<span></span>
</span>
diff --git a/2d/softbody/softbody_1/damped.cpp b/2d/softbody/softbody_1/damped.cpp
index 0344bd0..f56f346 100644
--- a/2d/softbody/softbody_1/damped.cpp
+++ b/2d/softbody/softbody_1/damped.cpp
@@ -52,13 +52,17 @@ namespace Damped {
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;
- void load(Renderer2d* renderer, DampedSpringWeight* inWieight, float32 length, float32 loopRadius, float32 initialDisplacement);
+ void load(Renderer2d* renderer, DampedSpringWeight* inWieight, float32 length, float32 loopRadius, float32 initialDisplacement, float32 inK, float32 inC);
void update(float32 dtSeconds);
void render(Renderer2d* renderer);
void unload();
@@ -92,7 +96,7 @@ namespace Damped {
renderer.load(context);
weight.load(&renderer, initVariables.mass, Vector4 { 55.f, 235.f, 35.f, 255.f }, Vector4 { 235.f, 5.f, 235.f, 255.f });
- spring.load(&renderer, &weight, initVariables.springLength, 16.f, initVariables.initialDisplacement);
+ spring.load(&renderer, &weight, initVariables.springLength, 16.f, initVariables.initialDisplacement, initVariables.k, initVariables.c);
mainLoop.run(update);
}
@@ -164,30 +168,105 @@ namespace Damped {
const float32 epsilon = 0.0001f;
- void DampedSpring::load(Renderer2d* renderer, DampedSpringWeight* inWeight, float32 length, float32 loopRadius, float32 initialDisplacement) {
- initialDisplacement = initialDisplacement;
+ void DampedSpring::load(Renderer2d* renderer, DampedSpringWeight* inWeight, float32 length, float32 loopRadius, float32 inInitialDisplacement, float32 inK, float32 inC) {
+ initialDisplacement = inInitialDisplacement;
weight = inWeight;
- discriminant = c * c - (4 * weight->mass * k);
+ k = inK;
+ c = inC;
- if (discriminant < epsilon && discriminant > -epsilon) { // Real repeated root (~ zero): Overdamped motion
- printf("Overdamped motion.\n");
- type = DampedSpringType::Overdamped;
- }
- else if (discriminant > 0) { // Two real roots (greater than zero): Critically damped motion
+ // Set the quadratic terms to something that we're familiar with.
+ float32 A = weight->mass;
+ float32 B = c;
+ float32 C = k;
+
+
+ discriminant = B * B - (4 * A * C);
+ timeElapsed = 0;
+ displacement = 0;
+
+ if (discriminant < epsilon && discriminant > -epsilon) {
+ // Real repeated root (~ zero): Critically damped motion
printf("Critically damped motion.\n");
- type = DampedSpringType::Critical;
+
+ 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 { // Complex pair (less than zero): Underdamped motion
+ 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;
- omega1 = sqrtf(-discriminant) / (2.f * weight->mass); // Note that we negate the discriminant to get the REAL positive part.
+ 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);
}
-
-
- timeElapsed = 0.f;
-
const int32 verticesPerSegment = 6;
numSegments = 256;
numVertices = numSegments * verticesPerSegment;
@@ -226,16 +305,21 @@ namespace Damped {
float32 lastDisplacement = displacement;
- if (discriminant < epsilon && discriminant > -epsilon) { // Real repeated root: Overdamped motion
-
- }
- else if (discriminant > 0) { // Two real roots: Critically damped motion
-
- }
- else { // Complex pair (less than zero): Underdamped motion
- float32 exponent = (-c / (2 * weight->mass)) * timeElapsed;
+ 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;
int32 vidx = 0;
diff --git a/2d/softbody/softbody_1/damped.h b/2d/softbody/softbody_1/damped.h
index eeb4aa9..47ae0ef 100644
--- a/2d/softbody/softbody_1/damped.h
+++ b/2d/softbody/softbody_1/damped.h
@@ -9,6 +9,7 @@ namespace Damped {
float32 initialDisplacement = 10.f;
float32 mass = 1.f;
float32 k = 4.f;
+ float32 c = 1.f;
};
void init(WebglContext* inContext);
diff --git a/2d/softbody/softbody_1/dist/output.js b/2d/softbody/softbody_1/dist/output.js
index a304400..9de60fb 100644
--- a/2d/softbody/softbody_1/dist/output.js
+++ b/2d/softbody/softbody_1/dist/output.js
@@ -3105,6 +3105,9 @@ var _Damped_SetK = Module["_Damped_SetK"] = createExportWrapper("Damped_SetK");
var _Damped_SetMass = Module["_Damped_SetMass"] = createExportWrapper("Damped_SetMass");
/** @type {function(...*):?} */
+var _Damped_SetC = Module["_Damped_SetC"] = createExportWrapper("Damped_SetC");
+
+/** @type {function(...*):?} */
var _main = Module["_main"] = createExportWrapper("main");
/** @type {function(...*):?} */
diff --git a/2d/softbody/softbody_1/dist/output.wasm b/2d/softbody/softbody_1/dist/output.wasm
index 19696f3..4c82a10 100755
--- a/2d/softbody/softbody_1/dist/output.wasm
+++ b/2d/softbody/softbody_1/dist/output.wasm
Binary files differ
diff --git a/2d/softbody/softbody_1/main.cpp b/2d/softbody/softbody_1/main.cpp
index 66792d3..355ba1c 100644
--- a/2d/softbody/softbody_1/main.cpp
+++ b/2d/softbody/softbody_1/main.cpp
@@ -65,4 +65,10 @@ extern "C" {
initVariables.mass = mass;
Damped::setInitVariables(initVariables);
}
+
+ EMSCRIPTEN_KEEPALIVE void Damped_SetC(float c) {
+ Damped::DampedInitVariables initVariables = Damped::getInitVariables();
+ initVariables.c = c;
+ Damped::setInitVariables(initVariables);
+ }
}
generated by cgit v1.2.1 (git 2.18.0) at 2024-10-18 15:25:48 +0000