Embedded Files
UMN CSCI 5611 Summer 2020 with Stephen J Guy
Emma Spindler <spindl038> and Parker Patterson <patte591>
Introduction
Introduction
Welcome to the website for our 3D cloth simulation! On this page you will find a discussion of some of the difficulties we encountered, our code, and a few demos of our simulation.
Designing the Simulation
Designing the Simulation
Overall, we had a fairly easy time designing the cloth simulation, though there were a few snags. We both found that working together was highly productive, since our respective attitudes and aptitudes were complementary, and, together, we had a wide array of skills at our disposal.
From the beginning, we knew we wanted to make a 3D cloth simulation. We decided the best way to begin was by simulating multiple swinging ropes, then adding horizontal forces between nodes in the ropes. We had some trouble at this stage of the project when it came to iterating over the nodes and ropes in the simulation -- mostly related to +1s and -1s. Once we got horizontal and vertical spring forces worked out, we switched our attention to tuning the cloth to be more realistic-looking. This part of the project was primarily undertaken by Emma. It was somewhat challenging for her to keep track of the many forces and equations in the simulation as she endeavored to achieve lifelike cloth behavior.
While Emma was tuning the simulation parameters, Parker went to work on texturing and lighting for the simulation. Implementing lighting was fairly simple once we understood the way the directionalLight() function works in Processing. Initially, the simulation only displayed the cloth using balls and strings, but, in order to simulate cloth more realistically, it was necessary to texture our stick-and-ball frame using a stock image found on the internet. We noted that there was a major improvement in simulation speed once we switched from wireframe to texture. Getting the texture to render properly was a bit of a challenge, but, with the help of a YouTube video, Parker learned about the TRIANGLE_STRIP option for the beginShape() function. Using TRIANGLE_STRIP was a major breakthrough in our effort to texture the cloth.
After texturing the cloth, our next step was to implement user-interaction and collision. For user-interaction, we decided to include an obstacle (a sphere) that follows the user’s cursor. We had no trouble implementing the obstacle thanks to Processing’s built-in I/O tools, but we found it quite difficult to implement collision. Detecting collision was easy, but implementing the physics of deflection was very challenging. After a lot of tinkering, we finally arrived at a solution for deflection physics. We did not have time to implement a version of collision that takes into account the triangular shape of our cloth texture tiles, so, at times, the sphere pokes through the cloth slightly. Additionally, there is an issue with parts of the cloth "spiking" when they collide with the obstacle. We are not exactly sure what causes this issue, but we think it may have something to do with the way we calculate the new position for nodes when they intersect with the sphere.
The Code
The Code
3D Vector Library
3D Vector Library
//Vector Library [3D]//CSCI 5611 Vector 3 Library [Incomplete]
//Instructions: Add 3D versions of all of the 2D vector functions// Vec3 must also support the cross product.
//Influenced by://CSCI 5611 Mouse Following with Vec2 [Starter]// Stephen J. Guy <sjguy@umn.edu>
public class Vec3 { public float x, y, z; public Vec3(float x, float y, float z){ this.x = x; this.y = y; this.z = z; } public String toString(){ return "(" + x+ ", " + y +","+ z+")"; } public float length(){ return sqrt(x*x + y*y + z*z); } public Vec3 plus(Vec3 rhs){ return new Vec3(x+rhs.x,y+rhs.y,z+rhs.z); } public void add(Vec3 rhs){ x += rhs.x; y += rhs.y; z += rhs.z; } public Vec3 minus(Vec3 rhs){ return new Vec3(x-rhs.x,y-rhs.y,z-rhs.z); } public void subtract(Vec3 rhs){ x -= rhs.x; y -= rhs.y; z -= rhs.z; } public Vec3 times(float rhs){ return new Vec3(x*rhs, y*rhs, z*rhs); } public void mul(float rhs){ x *= rhs; y *= rhs; z *= rhs; } public void normalize(){ float magnitude = sqrt(x*x + y*y + z*z); x /= magnitude; y /= magnitude; z /= magnitude; } public Vec3 normalized(){ float magnitude = sqrt(x*x + y*y + z*z); return new Vec3(x/magnitude, y/magnitude, z/magnitude); } public float distanceTo(Vec3 rhs){ float dx = rhs.x - x; float dy = rhs.y - y; float dz = rhs.z - z; return sqrt(dx*dx + dy*dy + dz*dz); }}
Vec3 interpolate(Vec3 a, Vec3 b, float t){ return new Vec3(0.0,0.0,0.0); }
float dot(Vec3 a, Vec3 b){ return a.x*b.x + a.y*b.y + a.z*b.z;}
Vec3 cross(Vec3 a, Vec3 b){ return new Vec3(a.y*b.z - a.z*b.y, a.z*b.x - a.x*b.z, a.x*b.y - a.y*b.x);}
Vec3 projAB(Vec3 a, Vec3 b){ return b.times(a.x*b.x + a.y*b.y + a.z*b.z);}
//Instructions: Add 3D versions of all of the 2D vector functions// Vec3 must also support the cross product.
//Influenced by://CSCI 5611 Mouse Following with Vec2 [Starter]// Stephen J. Guy <sjguy@umn.edu>
public class Vec3 { public float x, y, z; public Vec3(float x, float y, float z){ this.x = x; this.y = y; this.z = z; } public String toString(){ return "(" + x+ ", " + y +","+ z+")"; } public float length(){ return sqrt(x*x + y*y + z*z); } public Vec3 plus(Vec3 rhs){ return new Vec3(x+rhs.x,y+rhs.y,z+rhs.z); } public void add(Vec3 rhs){ x += rhs.x; y += rhs.y; z += rhs.z; } public Vec3 minus(Vec3 rhs){ return new Vec3(x-rhs.x,y-rhs.y,z-rhs.z); } public void subtract(Vec3 rhs){ x -= rhs.x; y -= rhs.y; z -= rhs.z; } public Vec3 times(float rhs){ return new Vec3(x*rhs, y*rhs, z*rhs); } public void mul(float rhs){ x *= rhs; y *= rhs; z *= rhs; } public void normalize(){ float magnitude = sqrt(x*x + y*y + z*z); x /= magnitude; y /= magnitude; z /= magnitude; } public Vec3 normalized(){ float magnitude = sqrt(x*x + y*y + z*z); return new Vec3(x/magnitude, y/magnitude, z/magnitude); } public float distanceTo(Vec3 rhs){ float dx = rhs.x - x; float dy = rhs.y - y; float dz = rhs.z - z; return sqrt(dx*dx + dy*dy + dz*dz); }}
Vec3 interpolate(Vec3 a, Vec3 b, float t){ return new Vec3(0.0,0.0,0.0); }
float dot(Vec3 a, Vec3 b){ return a.x*b.x + a.y*b.y + a.z*b.z;}
Vec3 cross(Vec3 a, Vec3 b){ return new Vec3(a.y*b.z - a.z*b.y, a.z*b.x - a.x*b.z, a.x*b.y - a.y*b.x);}
Vec3 projAB(Vec3 a, Vec3 b){ return b.times(a.x*b.x + a.y*b.y + a.z*b.z);}
Cloth Simulation
Cloth Simulation
// CSCI 5611 Project 2: Cloth Simulation// Copyright 2020 Emma Spindler and Parker Patterson. All rights reserved.// <spindl038> <patte591>// Summer 2020
// Portions of this code are borrowed from Stephen J. Guy's "Swinging Rope" example for CSCI 5611
// Simulation Parametersfloat floor; // floor = height; see setup()float gravity = 200;int maxNodes = 100;int numVertices = 80; int numRopes = numVertices;int numNodes = numVertices;PVector cameraPos;
boolean leftForceActive;boolean rightForceActive;boolean upForceActive;boolean downForceActive;float userForceSens = 1;
// Visualsboolean ballMode = false; // toggle with mouse1, mouse2PImage clothtex; // cloth texturefloat radius = 4;float sw = .5; // stroke weight
// Springs and massesfloat restLen; // restLen = floor*0.4/numVertices; see setup() (change this later)float mass = .2; //TRY-IT: How does changing mass affect resting length of the rope?float k = 200; //TRY-IT: How does changing k affect resting length of the rope?float kv = 50; //TRY-IT: How big can you make kv?float friction = .1;
// Obstacle//PShape sphere; float sphereRadius = 100;float sphereColor[] = {mouseX * 2, mouseY, 160};Vec3 spherePos = new Vec3(0,0,0);
// Top-left corner of clothfloat clothTopLeftX = 26;float clothTopLeftY = 26;float clothTopLeftZ = 26;
//Inital positions and velocities of massesfloat ballX[][] = new float[maxNodes][numRopes];float ballY[][] = new float[maxNodes][numRopes];float ballZ[][] = new float[maxNodes][numRopes];float velY[][] = new float[maxNodes][numRopes];float velX[][] = new float[maxNodes][numRopes];float velZ[][] = new float[maxNodes][numRopes];float accX[][] = new float[maxNodes][numRopes];float accY[][] = new float[maxNodes][numRopes];float accZ[][] = new float[maxNodes][numRopes];
PVector pos = new PVector();PVector vel = new PVector();PVector acc = new PVector();
void setup() { size(575, 700, P3D); camera(width/2, height/2, 700, // camera position width/2, height/2, 0, // center of scene 0, 1, 0); // environment parameters floor = height; restLen = .2*floor/numVertices; surface.setTitle("Stretchy Burlap"); clothtex = loadImage("cloth.jpg"); // obstacle initialization sphereColor[0] = mouseX * 2; sphereColor[1] = mouseY; sphereColor[2] = 255 - mouseX; spherePos.x = mouseX - .9*(width/2 - mouseX); spherePos.y = mouseY - .9*(height/2 - mouseY); spherePos.z = -350; //sphere = createShape(SPHERE, sphereRadius); //sphere.setFill(color(sphereColor[0],sphereColor[1],sphereColor[2]));
pos = new PVector(25, 25); vel = new PVector(0, 0); acc = new PVector(0, 0); leftForceActive = false; rightForceActive = false; upForceActive = false; downForceActive = false; for (int j = 0; j < numNodes; j++){ for (int i = 0; i < numRopes; i++){ if (j == 0){ // special case to make top row straight // TODO: simulation might be faster if we didn't have to make this check every loop ballX[j][i] = clothTopLeftX + (1/numVertices + 1)*7*i; ballY[j][i] = clothTopLeftY + restLen*j; ballZ[j][i] = clothTopLeftZ - 15*i; } else { ballX[j][i] = clothTopLeftX + (1/numVertices + 1)*7*i - random(2); ballY[j][i] = clothTopLeftY + restLen*j - random(2); ballZ[j][i] = clothTopLeftZ - 15*i - random(1); } velX[j][i] = 0; velY[j][i] = 0; velZ[j][i] = 0; } }}
void draw() { background(26); noCursor(); for(int i = 0; i < 20; i++) update(1/(60*frameRate)); // Lighting specular(127,127,127); // Main light source ambientLight(26,26,26); lightSpecular(127,127,127); // ?? directionalLight(200, 200, 200, -1, 1, -1); // obstacle pushMatrix(); //stroke(255, 50); translate(spherePos.x, spherePos.y, spherePos.z); //rotateX(mouseY * 0.05); //rotateY(mouseX * 0.05); fill(sphereColor[0], sphereColor[1], sphereColor[2]); //sphereDetail(mouseX / 4); sphere(sphereRadius); popMatrix(); //cloth if (ballMode){ fill(100); for (int j = 0; j < numNodes-1; j++){ for (int i = 0; i < numRopes-1; i++){ pushMatrix(); stroke(127); strokeWeight(sw); line(ballX[j][i],ballY[j][i],ballZ[j][i],ballX[j+1][i],ballY[j+1][i],ballZ[j+1][i]); line(ballX[j][i],ballY[j][i],ballZ[j][i],ballX[j][i+1],ballY[j][i+1],ballZ[j][i+1]); noStroke(); translate(ballX[j+1][i],ballY[j+1][i],ballZ[j+1][i]); sphere(radius); popMatrix(); } } } else { noStroke(); for (int i = 0; i < numNodes - 1; i++){ beginShape(TRIANGLE_STRIP); // TRIANGLE_STRIP takes two rows of points and tiles them with triangles texture(clothtex); for (int j = 0; j < numRopes - 1; j++){ vertex(ballX[i][j], ballY[i][j], ballZ[i][j], j*clothtex.width/numRopes, i*clothtex.height/numNodes); vertex(ballX[i+1][j], ballY[i+1][j], ballZ[i+1][j], j*clothtex.width/numRopes, (i+1)*clothtex.height/numNodes); } endShape(); } }}
void update(float dt){ sphereColor[0] += mouseX * 2; sphereColor[1] = mouseY; sphereColor[2] = 255 - mouseX; spherePos.x = mouseX - .9*(width/2 - mouseX); spherePos.y = mouseY - .9*(height/2 - mouseY); spherePos.z = -450; //camera.Update(dt); // Compute (damped) Hooke's law for each spring // vertical forces for (int j = 0; j < numNodes - 1; j++){ for (int i = 0; i < numRopes; i++){ float stringdx = (ballX[j+1][i] - ballX[j][i]); float stringdy = (ballY[j+1][i] - ballY[j][i]); float stringdz = (ballZ[j+1][i] - ballZ[j][i]); float stringLen = sqrt(stringdx*stringdx + stringdy*stringdy + stringdz*stringdz); float stringF = -k*(stringLen - restLen); // vertical force float stringdirX = stringdx/stringLen; float stringdirY = stringdy/stringLen; float stringdirZ = stringdz/stringLen; float projVbot = velX[j][i]*stringdirX + velY[j][i]*stringdirY + velZ[j][i]*stringdirZ; float projVtop = velX[j+1][i]*stringdirX + velY[j+1][i]*stringdirY + velZ[j+1][i]*stringdirZ; float dampF = -kv*(projVtop - projVbot);
float forceX = (stringF+dampF)*stringdirX; float forceY = (stringF+dampF)*stringdirY; float forceZ = (stringF+dampF)*stringdirZ;
accX[j][i] -= .5*forceX/mass; accY[j][i] -= .5*forceY/mass; accZ[j][i] -= .5*forceZ/mass; accX[j+1][i] = .5*forceX/mass; accY[j+1][i] = .5*forceY/mass; accZ[j+1][i] = .5*forceZ/mass; } } // horizontal forces for (int j = 0; j < numNodes; j++){ for (int i = 0; i < numRopes - 1; i++){ float stringdx = (ballX[j][i+1] - ballX[j][i]); float stringdy = (ballY[j][i+1] - ballY[j][i]); float stringdz = (ballZ[j][i+1] - ballZ[j][i]); float stringLen = sqrt(stringdx*stringdx + stringdy*stringdy + stringdz*stringdz); float stringF = -k*(stringLen - restLen); float stringdirX = stringdx/stringLen; float stringdirY = stringdy/stringLen; float stringdirZ = stringdz/stringLen; float projVbot = velX[j][i]*stringdirX + velY[j][i]*stringdirY + velZ[j][i]*stringdirZ; float projVtop = velX[j][i+1]*stringdirX + velY[j][i+1]*stringdirY + velZ[j+1][i]*stringdirZ; float dampF = -kv*(projVtop - projVbot); float forceX = (stringF+dampF)*stringdirX; float forceY = (stringF+dampF)*stringdirY; float forceZ = (stringF+dampF)*stringdirZ; accX[j][i] -= .5*forceX/mass; accY[j][i] -= .5*forceY/mass; accZ[j][i] -= .5*forceZ/mass; accX[j][i+1] += .5*forceX/mass; accY[j][i+1] += .5*forceY/mass; accZ[j+1][i] += .5*forceZ/mass; } }
//Eulerian integration for (int j = 1; j < numNodes; j++){ for (int i = 0; i < numRopes; i++){ velX[j][i] += accX[j][i]*dt; ballX[j][i] += velX[j][i]*dt; velY[j][i] += (accY[j][i]+gravity)*dt; ballY[j][i] += velY[j][i]*dt;// } }
//Collision detection and response // obstacle for (int j = 0; j <numNodes; j++){ for (int i = 0; i < numRopes; i++){ Vec3 nodePos = new Vec3(ballX[j][i], ballY[j][i], ballZ[j][i]); // get PVector version of node's position float distance = spherePos.distanceTo(nodePos); // calculate distance if (distance < sphereRadius + .09){ // if the distance between the sphere's edge and the node is less than .09: Vec3 sphereNormal = spherePos.minus(nodePos); sphereNormal.normalize(); // calculate sphere normal Vec3 nodeVel = new Vec3(velX[j][i], velY[j][i], velZ[j][i]); // get PVector version of node's velocity Vec3 bounce = sphereNormal.times(dot(nodeVel, sphereNormal)); // calculate bounce vector velX[j][i] = -1.5*bounce.x; // update velocity velY[j][i] = -1.5*bounce.y; velZ[j][i] = -1.5*bounce.z; Vec3 spheretoPoint = nodePos.minus(spherePos); spheretoPoint.normalize(); spheretoPoint = spheretoPoint.times(sphereRadius); Vec3 worldPeace = new Vec3((spherePos.x + spheretoPoint.x), (spherePos.y+spheretoPoint.y), (spherePos.z+spheretoPoint.z)); ballX[j][i] = worldPeace.x; // update position of node ballY[j][i] = worldPeace.y; ballZ[j][i] = worldPeace.z; } } } // floor for (int j = 0; j <numNodes; j++){ for (int i = 0; i < numRopes; i++){ if (ballY[j][i]+radius > floor){ velY[j][i] *= -.9; ballY[j][i] = floor - radius; } } }}
void mousePressed(){ if (mouseButton == LEFT) ballMode = !ballMode;}
// Portions of this code are borrowed from Stephen J. Guy's "Swinging Rope" example for CSCI 5611
// Simulation Parametersfloat floor; // floor = height; see setup()float gravity = 200;int maxNodes = 100;int numVertices = 80; int numRopes = numVertices;int numNodes = numVertices;PVector cameraPos;
boolean leftForceActive;boolean rightForceActive;boolean upForceActive;boolean downForceActive;float userForceSens = 1;
// Visualsboolean ballMode = false; // toggle with mouse1, mouse2PImage clothtex; // cloth texturefloat radius = 4;float sw = .5; // stroke weight
// Springs and massesfloat restLen; // restLen = floor*0.4/numVertices; see setup() (change this later)float mass = .2; //TRY-IT: How does changing mass affect resting length of the rope?float k = 200; //TRY-IT: How does changing k affect resting length of the rope?float kv = 50; //TRY-IT: How big can you make kv?float friction = .1;
// Obstacle//PShape sphere; float sphereRadius = 100;float sphereColor[] = {mouseX * 2, mouseY, 160};Vec3 spherePos = new Vec3(0,0,0);
// Top-left corner of clothfloat clothTopLeftX = 26;float clothTopLeftY = 26;float clothTopLeftZ = 26;
//Inital positions and velocities of massesfloat ballX[][] = new float[maxNodes][numRopes];float ballY[][] = new float[maxNodes][numRopes];float ballZ[][] = new float[maxNodes][numRopes];float velY[][] = new float[maxNodes][numRopes];float velX[][] = new float[maxNodes][numRopes];float velZ[][] = new float[maxNodes][numRopes];float accX[][] = new float[maxNodes][numRopes];float accY[][] = new float[maxNodes][numRopes];float accZ[][] = new float[maxNodes][numRopes];
PVector pos = new PVector();PVector vel = new PVector();PVector acc = new PVector();
void setup() { size(575, 700, P3D); camera(width/2, height/2, 700, // camera position width/2, height/2, 0, // center of scene 0, 1, 0); // environment parameters floor = height; restLen = .2*floor/numVertices; surface.setTitle("Stretchy Burlap"); clothtex = loadImage("cloth.jpg"); // obstacle initialization sphereColor[0] = mouseX * 2; sphereColor[1] = mouseY; sphereColor[2] = 255 - mouseX; spherePos.x = mouseX - .9*(width/2 - mouseX); spherePos.y = mouseY - .9*(height/2 - mouseY); spherePos.z = -350; //sphere = createShape(SPHERE, sphereRadius); //sphere.setFill(color(sphereColor[0],sphereColor[1],sphereColor[2]));
pos = new PVector(25, 25); vel = new PVector(0, 0); acc = new PVector(0, 0); leftForceActive = false; rightForceActive = false; upForceActive = false; downForceActive = false; for (int j = 0; j < numNodes; j++){ for (int i = 0; i < numRopes; i++){ if (j == 0){ // special case to make top row straight // TODO: simulation might be faster if we didn't have to make this check every loop ballX[j][i] = clothTopLeftX + (1/numVertices + 1)*7*i; ballY[j][i] = clothTopLeftY + restLen*j; ballZ[j][i] = clothTopLeftZ - 15*i; } else { ballX[j][i] = clothTopLeftX + (1/numVertices + 1)*7*i - random(2); ballY[j][i] = clothTopLeftY + restLen*j - random(2); ballZ[j][i] = clothTopLeftZ - 15*i - random(1); } velX[j][i] = 0; velY[j][i] = 0; velZ[j][i] = 0; } }}
void draw() { background(26); noCursor(); for(int i = 0; i < 20; i++) update(1/(60*frameRate)); // Lighting specular(127,127,127); // Main light source ambientLight(26,26,26); lightSpecular(127,127,127); // ?? directionalLight(200, 200, 200, -1, 1, -1); // obstacle pushMatrix(); //stroke(255, 50); translate(spherePos.x, spherePos.y, spherePos.z); //rotateX(mouseY * 0.05); //rotateY(mouseX * 0.05); fill(sphereColor[0], sphereColor[1], sphereColor[2]); //sphereDetail(mouseX / 4); sphere(sphereRadius); popMatrix(); //cloth if (ballMode){ fill(100); for (int j = 0; j < numNodes-1; j++){ for (int i = 0; i < numRopes-1; i++){ pushMatrix(); stroke(127); strokeWeight(sw); line(ballX[j][i],ballY[j][i],ballZ[j][i],ballX[j+1][i],ballY[j+1][i],ballZ[j+1][i]); line(ballX[j][i],ballY[j][i],ballZ[j][i],ballX[j][i+1],ballY[j][i+1],ballZ[j][i+1]); noStroke(); translate(ballX[j+1][i],ballY[j+1][i],ballZ[j+1][i]); sphere(radius); popMatrix(); } } } else { noStroke(); for (int i = 0; i < numNodes - 1; i++){ beginShape(TRIANGLE_STRIP); // TRIANGLE_STRIP takes two rows of points and tiles them with triangles texture(clothtex); for (int j = 0; j < numRopes - 1; j++){ vertex(ballX[i][j], ballY[i][j], ballZ[i][j], j*clothtex.width/numRopes, i*clothtex.height/numNodes); vertex(ballX[i+1][j], ballY[i+1][j], ballZ[i+1][j], j*clothtex.width/numRopes, (i+1)*clothtex.height/numNodes); } endShape(); } }}
void update(float dt){ sphereColor[0] += mouseX * 2; sphereColor[1] = mouseY; sphereColor[2] = 255 - mouseX; spherePos.x = mouseX - .9*(width/2 - mouseX); spherePos.y = mouseY - .9*(height/2 - mouseY); spherePos.z = -450; //camera.Update(dt); // Compute (damped) Hooke's law for each spring // vertical forces for (int j = 0; j < numNodes - 1; j++){ for (int i = 0; i < numRopes; i++){ float stringdx = (ballX[j+1][i] - ballX[j][i]); float stringdy = (ballY[j+1][i] - ballY[j][i]); float stringdz = (ballZ[j+1][i] - ballZ[j][i]); float stringLen = sqrt(stringdx*stringdx + stringdy*stringdy + stringdz*stringdz); float stringF = -k*(stringLen - restLen); // vertical force float stringdirX = stringdx/stringLen; float stringdirY = stringdy/stringLen; float stringdirZ = stringdz/stringLen; float projVbot = velX[j][i]*stringdirX + velY[j][i]*stringdirY + velZ[j][i]*stringdirZ; float projVtop = velX[j+1][i]*stringdirX + velY[j+1][i]*stringdirY + velZ[j+1][i]*stringdirZ; float dampF = -kv*(projVtop - projVbot);
float forceX = (stringF+dampF)*stringdirX; float forceY = (stringF+dampF)*stringdirY; float forceZ = (stringF+dampF)*stringdirZ;
accX[j][i] -= .5*forceX/mass; accY[j][i] -= .5*forceY/mass; accZ[j][i] -= .5*forceZ/mass; accX[j+1][i] = .5*forceX/mass; accY[j+1][i] = .5*forceY/mass; accZ[j+1][i] = .5*forceZ/mass; } } // horizontal forces for (int j = 0; j < numNodes; j++){ for (int i = 0; i < numRopes - 1; i++){ float stringdx = (ballX[j][i+1] - ballX[j][i]); float stringdy = (ballY[j][i+1] - ballY[j][i]); float stringdz = (ballZ[j][i+1] - ballZ[j][i]); float stringLen = sqrt(stringdx*stringdx + stringdy*stringdy + stringdz*stringdz); float stringF = -k*(stringLen - restLen); float stringdirX = stringdx/stringLen; float stringdirY = stringdy/stringLen; float stringdirZ = stringdz/stringLen; float projVbot = velX[j][i]*stringdirX + velY[j][i]*stringdirY + velZ[j][i]*stringdirZ; float projVtop = velX[j][i+1]*stringdirX + velY[j][i+1]*stringdirY + velZ[j+1][i]*stringdirZ; float dampF = -kv*(projVtop - projVbot); float forceX = (stringF+dampF)*stringdirX; float forceY = (stringF+dampF)*stringdirY; float forceZ = (stringF+dampF)*stringdirZ; accX[j][i] -= .5*forceX/mass; accY[j][i] -= .5*forceY/mass; accZ[j][i] -= .5*forceZ/mass; accX[j][i+1] += .5*forceX/mass; accY[j][i+1] += .5*forceY/mass; accZ[j+1][i] += .5*forceZ/mass; } }
//Eulerian integration for (int j = 1; j < numNodes; j++){ for (int i = 0; i < numRopes; i++){ velX[j][i] += accX[j][i]*dt; ballX[j][i] += velX[j][i]*dt; velY[j][i] += (accY[j][i]+gravity)*dt; ballY[j][i] += velY[j][i]*dt;// } }
//Collision detection and response // obstacle for (int j = 0; j <numNodes; j++){ for (int i = 0; i < numRopes; i++){ Vec3 nodePos = new Vec3(ballX[j][i], ballY[j][i], ballZ[j][i]); // get PVector version of node's position float distance = spherePos.distanceTo(nodePos); // calculate distance if (distance < sphereRadius + .09){ // if the distance between the sphere's edge and the node is less than .09: Vec3 sphereNormal = spherePos.minus(nodePos); sphereNormal.normalize(); // calculate sphere normal Vec3 nodeVel = new Vec3(velX[j][i], velY[j][i], velZ[j][i]); // get PVector version of node's velocity Vec3 bounce = sphereNormal.times(dot(nodeVel, sphereNormal)); // calculate bounce vector velX[j][i] = -1.5*bounce.x; // update velocity velY[j][i] = -1.5*bounce.y; velZ[j][i] = -1.5*bounce.z; Vec3 spheretoPoint = nodePos.minus(spherePos); spheretoPoint.normalize(); spheretoPoint = spheretoPoint.times(sphereRadius); Vec3 worldPeace = new Vec3((spherePos.x + spheretoPoint.x), (spherePos.y+spheretoPoint.y), (spherePos.z+spheretoPoint.z)); ballX[j][i] = worldPeace.x; // update position of node ballY[j][i] = worldPeace.y; ballZ[j][i] = worldPeace.z; } } } // floor for (int j = 0; j <numNodes; j++){ for (int i = 0; i < numRopes; i++){ if (ballY[j][i]+radius > floor){ velY[j][i] *= -.9; ballY[j][i] = floor - radius; } } }}
void mousePressed(){ if (mouseButton == LEFT) ballMode = !ballMode;}
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