CircleCount vous aide à mieux comprendre Google +
Description
This animation uses a 12-12-3 Archimedean tiling, with circles as vertices. Three distinct arrays are constructed and used to rotate symmetrical sub-groupings of the tiling's vertices (3,6,18) during the animation. Because I tend to convert many of my 2D animations into 3D ones and because Processing's PVector class is irritatingly mutable, I use the 3-space classes from Apache Commons library for vectors and rotations.
This animation is dedicated to Corina Marinescu for her impressive contributions on G+ and because she's a wonderful inimitable character:
+CorinaMarinescu
If you enjoy this animation, are interested in seeing others or would like to ask any questions, please visit me on G+:
+SeanWalker67
This animation is dedicated to Corina Marinescu for her impressive contributions on G+ and because she's a wonderful inimitable character:
+CorinaMarinescu
If you enjoy this animation, are interested in seeing others or would like to ask any questions, please visit me on G+:
+SeanWalker67
What is this all about?
Processing is an open source programming language.
As you can see here, it is embeddable on a website by using Processing.js.
Check out also the Google+ Page +Processing and their Google+ Community.
As you can see here, it is embeddable on a website by using Processing.js.
Check out also the Google+ Page +Processing and their Google+ Community.
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import java.util.*;
import processing.core.*;
import processing.opengl.*;
import org.apache.commons.math3.geometry.*;
import org.apache.commons.math3.geometry.euclidean.threed.*;
// ------------------------------------------------------------------------------------------------
// 12 circle based tiling pattern based Processing Sketch - dedicated to Corina Marinescu
// Jan 1, 2016
// - Developed using Processing 3.0, but in Eclipse
// - Two class files including this one and Circle.java
// - Uses the Apache Math Common library for Vector3D and Rotation classes
// -------------------------------------------------------------------------------------------------
public class MyProcessingSketch extends PApplet {
final static double framesPerCycle = 160;
Vector3D eye = new Vector3D(100, -500, 100);
final int circUnitPatternNum = 3;
final int rows = 12;
final int cols = 28;
float radius = 30;
float radFract = 0.7f;
int circNumPerTrio = 3;
int circNumPerSix = 6;
int threesPerEighteen = 6;
final int eighteensRows = (rows-1)/2;
final int eighteensCols = cols/3;
// Component angles and vectors for the 12 point circles of the tiling pattern
double compAngles[] = {(11d/12d)*TWO_PI, (10d/12d)*TWO_PI, (9d/12d)*TWO_PI, (8d/12d)*TWO_PI, (7d/12d)*TWO_PI, (6d/12d)*TWO_PI,
(5d/12d)*TWO_PI, (4d/12d)*TWO_PI, (3d/12d)*TWO_PI, (2d/12d)*TWO_PI, (1d/12d)*TWO_PI, (0d/12d)*TWO_PI};
Vector3D vComps[] =
{ new Vector3D(Math.cos(compAngles[0]), Math.sin(compAngles[0]), 0).scalarMultiply(radius), new Vector3D(Math.cos(compAngles[1]), Math.sin(compAngles[1]), 0).scalarMultiply(radius),
new Vector3D(Math.cos(compAngles[2]), Math.sin(compAngles[2]), 0).scalarMultiply(radius), new Vector3D(Math.cos(compAngles[3]), Math.sin(compAngles[3]), 0).scalarMultiply(radius),
new Vector3D(Math.cos(compAngles[4]), Math.sin(compAngles[4]), 0).scalarMultiply(radius), new Vector3D(Math.cos(compAngles[5]), Math.sin(compAngles[5]), 0).scalarMultiply(radius),
new Vector3D(Math.cos(compAngles[6]), Math.sin(compAngles[6]), 0).scalarMultiply(radius), new Vector3D(Math.cos(compAngles[7]), Math.sin(compAngles[7]), 0).scalarMultiply(radius),
new Vector3D(Math.cos(compAngles[8]), Math.sin(compAngles[8]), 0).scalarMultiply(radius), new Vector3D(Math.cos(compAngles[9]), Math.sin(compAngles[9]), 0).scalarMultiply(radius),
new Vector3D(Math.cos(compAngles[10]), Math.sin(compAngles[10]), 0).scalarMultiply(radius), new Vector3D(Math.cos(compAngles[11]), Math.sin(compAngles[11]), 0).scalarMultiply(radius)};
// arrays for grouping the subsets of the tiling that are rotated: trio circle is prime, the other two are derived with the 'group' methods
Circle trioCircles[][][] = new Circle[cols][rows][circUnitPatternNum];
Circle eighteensCircles[][][][] = new Circle[cols/3][rows/2][threesPerEighteen][];
Circle sixCircles[][][] = new Circle[cols/2-2][rows-2][circNumPerSix];
// vectors offsets for generating the tiling pattern - based on 3 circle groups (trios) of the circle
Vector3D vertUnitDisp[][] = new Vector3D[2][2];
Vector3D horUnitDisp[][] = new Vector3D[2][2];
public static void main(String args[]) {
PApplet.main(new String[] { "--present", "MyProcessingSketch" });
}
public void settings() {
// In Processing 3.0 it's necessary to set the graphics mode in the settings() method outside of the Processing env
size(800, 600, "processing.opengl.PGraphics2D");
}
public void setup() {
vertUnitDisp[0][0] = vComps[1].add(vComps[2]).add(vComps[3]);
vertUnitDisp[0][1] = vComps[1].add(vComps[2]).add(vComps[3]).add(vComps[4]).add(vComps[3]).add(vComps[2]).add(vComps[1]).add(vComps[0]);
vertUnitDisp[1][0] = vComps[1].add(vComps[2]).add(vComps[3]);
vertUnitDisp[1][1] = vComps[1].add(vComps[2]).add(vComps[3]).add(vComps[4]).add(vComps[3]).add(vComps[2]).add(vComps[1]).add(vComps[0]);
horUnitDisp[0][0] = vComps[11].add(vComps[10]);
horUnitDisp[0][1] = vComps[11].add(vComps[10]).add(vComps[11]).add(vComps[0]);
horUnitDisp[1][0] = vComps[11].add(vComps[0]);
horUnitDisp[1][1] = vComps[11].add(vComps[0]).add(vComps[11]).add(vComps[10]);
}
public void draw() {
// cycle (0,1] is the clock of the animation - 0 represents the start (or first frame) and 1 the final frame
float cycle = (float)((frameCount-1)/framesPerCycle);
// always draw a frame buffer - more flexible and retains alpha channel values unlike view
PGraphics pg = createGraphics(width,height,P3D);
pg.beginDraw();
// Make the center of the view window the center of pixel plane
pg.translate(0.5f*width, 0.5f*height, 0);
pg.background(0);
// Construct the tiling pattern within the trioCircles[][][] circles array
constructTiling(new Vector3D(0,0,0));
// Derive the array of sub-grouping with 18 circles
groupEighteens();
// Derive the array of sub-groupings with 6 circles
groupSixes();
// This animation sequence is devided into 6 segments
float segs = 6;
// Animation segmentation logic
if(cycle <= 1f/segs) { // Rotate 6 circle sub-groups
float cycle2 = smootherStep(0,1,map(cycle, 0f, 1f/segs, 0f, 1f));
rotateSixes(cycle2);
} else if(cycle <= 2f/segs) { // Rotate 3 circle sub-groups
float cycle2 = smootherStep(0,1,map(cycle, 1f/segs, 2f/segs, 0f, 1f));
rotateThrees(cycle2);
} else if (cycle <= 3f/segs){ // Rotate 18 circle sub-groups
float cycle2 = smootherStep(0,1,map(cycle, 2f/segs, 3f/segs, 0f, 1f));
rotateEighteens(cycle2);
} else if (cycle <= 4f/segs){ // Rotate 3 circle sub-groups within rotating 18 circle sub-groups
float cycle2 = smootherStep(0,1,map(cycle, 3f/segs, 4f/segs, 0, 1));
rotateThrees(-cycle2);
rotateEighteens(cycle2);
} else if (cycle <= 4.5f/segs){ // Half rotate 3 circle sub-groups
float cycle2 = smootherStep(0,1,map(cycle, 4f/segs, 4.5f/segs, 0, 0.5f));
rotateThrees(cycle2);
} else if (cycle <= 5.5f/segs){ // Half rotate 18 circle sub-groups with 3 cirle sub-groups fixed at half-rotation
float cycle2 = smootherStep(0,1,map(cycle, 4.5f/segs, 5.5f/segs, 0, 0.5f));
rotateThrees(0.5f);
rotateEighteens(cycle2);
} else { // Remove half rotation of 3 circle sub-groups
float cycle2 = smootherStep(0,1,map(cycle, 5.5f/segs, 6f/segs, 0.5f, 0));
rotateThrees(cycle2);
}
// Iterate through the circle tiling elements and draw them to the pixel buffer
drawTiling(pg);
pg.endDraw();
// Transfer the pixel buffer to the views pixel plane
image(pg,0,0);
println(frameCount);
if (frameCount == framesPerCycle) exit();
String strFileName = "C:\\Users\\Sean\\Documents\\Processing\\workspace\\OctagonalCircles\\images\\" + nf(frameCount, 3, 1) + ".gif";
pg.save(strFileName);
}
void drawTiling(PGraphics pg) {
for(int col=0; col<cols; col++) {
for(int row=0; row<rows; row++) {
for(int i=0; i<circNumPerTrio; i++) {
trioCircles[col][row][i].draw(pg);
}
}
}
}
void rotateThrees(float cycle) {
for(int col=0; col<cols; col++) {
for(int row=0; row<rows; row++) {
rotateThree(trioCircles[col][row][0], trioCircles[col][row][1], trioCircles[col][row][2], cycle);
}
}
}
void groupSixes() {
for(int col=0; col<cols/2-2; col++) {
for(int row=0; row<rows-2; row++) {
for(int i = 0; i < threesPerEighteen; i++) {
int colOff = (row%2 == 0) ? 1 : 2;
sixCircles[col][row][0] = trioCircles[col*2+colOff][row+1][0];
sixCircles[col][row][1] = trioCircles[col*2+colOff-1][row+1][2];
sixCircles[col][row][2] = trioCircles[col*2+colOff][row+1][1];
sixCircles[col][row][3] = trioCircles[col*2+colOff][row+2][1];
sixCircles[col][row][4] = trioCircles[col*2+colOff][row+1][2];
sixCircles[col][row][5] = trioCircles[col*2+colOff+1][row+1][0];
}
}
}
}
void rotateSixes(float cycle) {
for(int col=0; col<cols/2-2; col++) {
for(int row=0; row<rows-2; row++) {
rotateSix(col, row, cycle);
}
}
}
void rotateSix(int col, int row, float cycle) {
Vector3D xyNorm = new Vector3D(0,0,1);
Rotation rot = new Rotation(xyNorm, cycle*(1d/3d)*TWO_PI);
Vector3D sixCent = calculateSixCenter(col, row);
for(int i = 0; i < circNumPerSix; i++) {
sixCircles[col][row][i].pos = sixCircles[col][row][i].pos.subtract(sixCent);
sixCircles[col][row][i].pos = rot.applyTo(sixCircles[col][row][i].pos);
sixCircles[col][row][i].pos = sixCircles[col][row][i].pos.add(sixCent);
}
}
Vector3D calculateSixCenter(int col, int row) {
Vector3D cent = new Vector3D(0,0,0);
for(int i = 0; i < circNumPerSix; i++) {
cent = cent.add(sixCircles[col][row][i].pos);
}
return cent.scalarMultiply(1d/6d);
}
void groupEighteens() {
for(int col=0; col<eighteensCols; col++) {
for(int row=0; row<eighteensRows; row++) {
for(int i = 0; i < threesPerEighteen; i++) {
if(col*3 < cols && row*2+2 < rows) {
if(col%2==0) {
eighteensCircles[col][row][0] = trioCircles[col*3][row*2];
eighteensCircles[col][row][1] = trioCircles[col*3][row*2+1];
eighteensCircles[col][row][2] = trioCircles[col*3+1][row*2];
eighteensCircles[col][row][3] = trioCircles[col*3+1][row*2+1];
eighteensCircles[col][row][4] = trioCircles[col*3+2][row*2];
eighteensCircles[col][row][5] = trioCircles[col*3+2][row*2+1];
} else {
eighteensCircles[col][row][0] = trioCircles[col*3][row*2+1];
eighteensCircles[col][row][1] = trioCircles[col*3][row*2+2];
eighteensCircles[col][row][2] = trioCircles[col*3+1][row*2+1];
eighteensCircles[col][row][3] = trioCircles[col*3+1][row*2+2];
eighteensCircles[col][row][4] = trioCircles[col*3+2][row*2+1];
eighteensCircles[col][row][5] = trioCircles[col*3+2][row*2+2];
}
}
}
}
}
}
void rotateEighteens(float cycle) {
for(int col=0; col<eighteensCols; col++) {
for(int row=0; row<eighteensRows; row++) {
rotateEghteen(col, row, cycle);
}
}
}
void rotateEghteen(int col, int row, float cycle) {
Vector3D xyNorm = new Vector3D(0,0,1);
Rotation rot = new Rotation(xyNorm, cycle*(1d/3d)*TWO_PI);
Vector3D eighteenCent = calculateEighteenCenter(col, row);
for(int g = 0; g < threesPerEighteen; g++) {
for(int t = 0; t < 3; t++) {
eighteensCircles[col][row][g][t].pos = eighteensCircles[col][row][g][t].pos.subtract(eighteenCent);
eighteensCircles[col][row][g][t].pos = rot.applyTo(eighteensCircles[col][row][g][t].pos);
eighteensCircles[col][row][g][t].pos = eighteensCircles[col][row][g][t].pos.add(eighteenCent);
}
}
}
Vector3D calculateEighteenCenter(int col, int row) {
Vector3D cent = new Vector3D(0,0,0);
for(int g = 0; g < threesPerEighteen; g++) {
for(int t = 0; t < 3; t++) {
cent = cent.add(eighteensCircles[col][row][g][t].pos);
}
}
return cent.scalarMultiply(1d/18d);
}
void rotateThree(Circle c0, Circle c1, Circle c2, float cycle) {
Vector3D xyNorm = new Vector3D(0,0,1);
Rotation rot = new Rotation(xyNorm, cycle*(1d/3d)*TWO_PI);
Vector3D center = c0.pos.add(c1.pos).add(c2.pos).scalarMultiply(0.3333333);
c0.pos = c0.pos.subtract(center);
c1.pos = c1.pos.subtract(center);
c2.pos = c2.pos.subtract(center);
c0.pos = rot.applyTo(c0.pos);
c1.pos = rot.applyTo(c1.pos);
c2.pos = rot.applyTo(c2.pos);
c0.pos = c0.pos.add(center);
c1.pos = c1.pos.add(center);
c2.pos = c2.pos.add(center);
}
void constructTiling(Vector3D center) {
for(int col=0; col<cols; col++) {
for(int row=0; row<rows; row++) {
Vector3D vHDisp;
Vector3D vVDisp;
int colEvenVectMult = (col - col%2)/2 - cols/4;
int colOddVectMult = col%2;
int rowEvenVectMult = (row - row%2)/2 - rows/4;
int rowOddVectMult = row%2;
if(row%2 == 0) {
vHDisp = horUnitDisp[0][1].scalarMultiply(colEvenVectMult).add((horUnitDisp[0][0].scalarMultiply(colOddVectMult)));
vVDisp = vertUnitDisp[0][1].scalarMultiply(rowEvenVectMult).add((vertUnitDisp[0][0].scalarMultiply(rowOddVectMult)));
} else {
vHDisp = horUnitDisp[1][1].scalarMultiply(colEvenVectMult).add((horUnitDisp[1][0].scalarMultiply(colOddVectMult)));
vVDisp = vertUnitDisp[1][1].scalarMultiply(rowEvenVectMult).add((vertUnitDisp[1][0].scalarMultiply(rowOddVectMult)));
}
boolean up = (col%2==0)? true : false;
if((row%2==1)) up = !up;
createPattern(trioCircles[col][row], center.add(vHDisp.add(vVDisp)), up);
}
}
}
void createPattern(Circle trio[], Vector3D pos, boolean up) {
trio[0] = new Circle(this, pos, radius, radFract, 2f*(float)Math.PI, 0, color(200, 0, 0), 2, color(100));
if(up) {
trio[1] = new Circle(this, trio[0].pos.add(vComps[1]), radius, radFract, 2f*(float)Math.PI, 0, color(200, 0, 0), 2, color(100));
trio[2] = new Circle(this, trio[1].pos.add(vComps[9]), radius, radFract, 2f*(float)Math.PI, 0, color(200, 0, 0), 2, color(100));
} else {
trio[1] = new Circle(this, trio[0].pos.add(vComps[9]), radius, radFract, 2f*(float)Math.PI, 0, color(200, 0, 0), 2, color(100));
trio[2] = new Circle(this, trio[1].pos.add(vComps[1]), radius, radFract, 2f*(float)Math.PI, 0, color(200, 0, 0), 2, color(100));
}
}
// The smooth methods are S curve interpolation functions - generally I use them to produce more appealing accel/deccel motions
float smoothStep(float edge0, float edge1, float x)
{
// Scale, and clamp x to 0..1 range
x = map(x, edge0, edge1, 0.0f, 1.0f);
// Evaluate polynomial
return x*x*(3.0f - 2.0f*x);
}
float smootherStep(float edge0, float edge1, float x)
{
// Scale, and clamp x to 0..1 range
x = map(x, edge0, edge1, 0.0f, 1.0f);
// Evaluate polynomial
return x*x*x*(x*(x*6 - 15) + 10);
}
}
///////////////////////////////////////////////////////////////////////////
import processing.core.*;
import processing.opengl.*;
import org.apache.commons.math3.geometry.*;
import org.apache.commons.math3.geometry.euclidean.threed.*;
public class Circle {
PApplet pa;
Vector3D pos;
float radius;
float radFract;
float angle;
float angleOpen;
int fillCol;
float edgeWidth;
int edgeCol;
Circle(PApplet pa, Vector3D pos, float radius, float radFract, float angle, float angleOpen, int fillCol, float edgeWidth, int edgeCol) {
this.pa = pa;
this.pos = pos;
this.radius = radius;
this.radFract = radFract;
this.angle = angle;
this.angleOpen = angleOpen;
this.fillCol = fillCol;
this.edgeWidth = edgeWidth;
this.edgeCol = edgeCol;
}
void draw(PGraphics pg) {
pg.fill(fillCol);
pg.strokeWeight(edgeWidth);
pg.stroke(edgeCol);
pg.arc((float)pos.getX(),(float)pos.getY(), radius*radFract, radius*radFract, 0, 2f*(float)Math.PI);
}
}
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