I want to detect separate shapes as random-generated lines split the canvas. I saved line intersection points in separate arrays for x and y positions (same order), but don't know how to connect
points that complete multiple pieces of shapes .
Is there any way to detect nearby points to close a minimal possible shape whether it be a triangle, rectangle, or polygon (e.g., by using beginShape and endShape)?
If 1) is too complicated, is there any method to select 3 or more random points from an array?
Here's a sample image that has 4 lines splitting the canvas with their intersection points marked in red. I also saved the top and bottom points (marked in black) of each random-generated line, plus the four corners of the canvas in the same arrays for x and y positions separately (px, py).
Multiple lines split the canvas.
How to get shapes split by lines in Processing?
I was able to get all the intersection points, but having a problem with connecting them into separate shapes. Here's the Processing code that I am working on:
//Run in Processing.
//Press r to refresh.
//Top and bottom points are added to px and py when refreshed (filled in black).
//Intersection points are added to px and py when detected (filled in red).
int l = 4; //set number of lines
float[] r1 = new float[l];
float[] r2 = new float[l];
float[] px = {}; //array to save x positions of all possible points
float[] py = {}; //array to save y positions of all possible points
boolean added = false;
void setup(){
size(800, 800);
background(255);
refresh();
}
void draw(){
background(255);
stroke(0, 150, 255, 150);
strokeWeight(1);
for(int i=0; i < r1.length; i++){
for(int j=0; j < r1.length; j++){
if(i>j){
boolean hit = lineLine(r1[i], 0, r2[i], height, r1[j], 0, r2[j], height);
if (hit) stroke(255, 150, 0, 150);
else stroke(0, 150, 255, 150);
}
line(r1[i], 0, r2[i], height);
}
}
added = true;
print(px.length);
}
//source: http://jeffreythompson.org/collision-detection/line-line.php
boolean lineLine(float x1, float y1, float x2, float y2, float x3, float y3, float x4, float y4) {
// calculate the distance to intersection point
float uA = ((x4-x3)*(y1-y3) - (y4-y3)*(x1-x3)) / ((y4-y3)*(x2-x1) - (x4-x3)*(y2-y1));
float uB = ((x2-x1)*(y1-y3) - (y2-y1)*(x1-x3)) / ((y4-y3)*(x2-x1) - (x4-x3)*(y2-y1));
// if uA and uB are between 0-1, lines are colliding
if (uA >= 0 && uA <= 1 && uB >= 0 && uB <= 1) {
// optionally, draw a circle where the lines meet
float intersectionX = x1 + (uA * (x2-x1));
float intersectionY = y1 + (uA * (y2-y1));
fill(255,0,0);
noStroke();
ellipse(intersectionX,intersectionY, 20,20);
if(added==false){
px = append(px, intersectionX);
py = append(py, intersectionY);
}
return true;
}
return false;
}
void refresh(){
added = false;
px = new float[0];
py = new float[0];
r1 = new float[l];
r2 = new float[l];
px = append(px, 0);
py = append(py, 0);
px = append(px, 0);
py = append(py, height);
px = append(px, width);
py = append(py, 0);
px = append(px, width);
py = append(py, height);
for(int i=0; i< r1.length; i++){
r1[i] = random(800);
}
for(int i=0; i< r2.length; i++){
r2[i] = random(800);
}
for(int i=0; i < r1.length; i++){
stroke(0);
line(r1[i], 0, r2[i], height);
px = append(px, r1[i]);
py = append(py, 0);
px = append(px, r2[i]);
py = append(py, height);
}
}
void keyReleased() {
if (key == 'r') refresh();
}
If you want to draw a shape made of the intersection points only you're on the right track with beginShape()/endShape().
Currently it looks like you're placing all the points in px, py: the intersection points and also the points defining the lines used to compute the intersections in the first place.
You might want to separate the two, for example a couply of arrays for points defining lines only and another pair of x,y arrays for the intersection points only. You'd only need to iterated through the intersected coordinates to place vertex(x, y) calls inbetween beginShape()/endShape(). Here's a modified version of you code to illustrate the idea:
//Run in Processing.
//Press r to refresh.
//Top and bottom points are added to px and py when refreshed (filled in black).
//Intersection points are added to px and py when detected (filled in red).
int l = 4; //set number of lines
float[] r1 = new float[l];
float[] r2 = new float[l];
float[] px = {}; //array to save x positions of all possible points
float[] py = {}; //array to save y positions of all possible points
float[] ipx = {}; // array to save x for intersections only
float[] ipy = {}; // array to save y for intersections only
boolean added = false;
void setup(){
size(800, 800);
background(255);
refresh();
}
void draw(){
background(255);
stroke(0, 150, 255, 150);
strokeWeight(1);
for(int i=0; i < r1.length; i++){
for(int j=0; j < r1.length; j++){
if(i>j){
boolean hit = lineLine(r1[i], 0, r2[i], height, r1[j], 0, r2[j], height);
if (hit) stroke(255, 150, 0, 150);
else stroke(0, 150, 255, 150);
}
line(r1[i], 0, r2[i], height);
}
}
added = true;
// draw intersections
beginShape();
for(int i = 0 ; i < ipx.length; i++){
vertex(ipx[i], ipy[i]);
}
endShape();
//print(px.length);
//println(px.length, py.length);
}
//source: http://jeffreythompson.org/collision-detection/line-line.php
boolean lineLine(float x1, float y1, float x2, float y2, float x3, float y3, float x4, float y4) {
// calculate the distance to intersection point
float uA = ((x4-x3)*(y1-y3) - (y4-y3)*(x1-x3)) / ((y4-y3)*(x2-x1) - (x4-x3)*(y2-y1));
float uB = ((x2-x1)*(y1-y3) - (y2-y1)*(x1-x3)) / ((y4-y3)*(x2-x1) - (x4-x3)*(y2-y1));
// if uA and uB are between 0-1, lines are colliding
if (uA >= 0 && uA <= 1 && uB >= 0 && uB <= 1) {
// optionally, draw a circle where the lines meet
float intersectionX = x1 + (uA * (x2-x1));
float intersectionY = y1 + (uA * (y2-y1));
fill(255,0,0);
noStroke();
ellipse(intersectionX,intersectionY, 20,20);
if(added==false){
px = append(px, intersectionX);
py = append(py, intersectionY);
// store intersections
ipx = append(ipx, intersectionX);
ipy = append(ipy, intersectionY);
}
return true;
}
return false;
}
void refresh(){
added = false;
px = new float[0];
py = new float[0];
ipx = new float[0];
ipy = new float[0];
r1 = new float[l];
r2 = new float[l];
px = append(px, 0);
py = append(py, 0);
px = append(px, 0);
py = append(py, height);
px = append(px, width);
py = append(py, 0);
px = append(px, width);
py = append(py, height);
for(int i=0; i< r1.length; i++){
r1[i] = random(800);
}
for(int i=0; i< r2.length; i++){
r2[i] = random(800);
}
for(int i=0; i < r1.length; i++){
stroke(0);
line(r1[i], 0, r2[i], height);
px = append(px, r1[i]);
py = append(py, 0);
px = append(px, r2[i]);
py = append(py, height);
}
}
void keyReleased() {
if (key == 'r') refresh();
}
Bare in mind this simlpy draws the points in the order in which the intersections were computed. On a good day you'll get something like this:
It doesn't exclude the possiblity of polygons with the wrong vertex order (winding):
and you might be get convave polygons too.
If you only need the outer 'shell' of these intersection points you might need something like a convex hull algorithm
One option to at least visually split shapes might to use beginShape(TRIANGLES); with endShape(CLOSE); which should iterate through points and draw a triangle for every coordinate triplate, however given random points and number of interesections you might end up with a missing triangle or two (e.g. 6 points = 2 triangles, 7 points = 2 triangles and 1 point with no missing pairs)
The only other note I have is around syntax: arrays are ok to get started with but you might want to look into ArrayList and PVector. This would allow you to use a single dynamic array of PVector instances which have x, y properties.
Update
Overall the code can be simplified. If we take out the line intersection related code we can get away with something like:
int l = 4; //set number of random lines
float[] r1 = new float[l]; // random x top
float[] r2 = new float[l]; // random x bottom
void setup() {
size(800, 800);
strokeWeight(3);
stroke(0, 150, 255, 150);
refresh();
}
void draw() {
background(255);
// random lines
for (int i=0; i < r1.length; i++) {
line(r1[i], 0, r2[i], height);
}
// borders
line(0, 0, width, 0);
line(width, 0, width - 1, height - 1);
line(0, height - 1, width - 1, height - 1);
line(0, 0, 0, height - 1);
}
void refresh() {
r1 = new float[l];
r2 = new float[l];
for (int i=0; i< r1.length; i++) {
r1[i] = random(800);
r2[i] = random(800);
}
}
void keyReleased() {
if (key == 'r') refresh();
}
If we were to use a basic Line class and make use of PVector and ArrayList we could rewrite the above as:
int numRandomLines = 4;
ArrayList<PVector> points = new ArrayList<PVector>();
void setup() {
size(800, 800);
stroke(0, 150, 255, 150);
strokeWeight(3);
refresh();
}
void refresh(){
// remove previous points
points.clear();
//add borders
points.add(new PVector(0, 0)); points.add(new PVector(width, 0));
points.add(new PVector(width, 0));points.add(new PVector(width - 1, height - 1));
points.add(new PVector(0, height - 1));points.add(new PVector(width - 1, height - 1));
points.add(new PVector(0, 0)); points.add(new PVector(0, height - 1));
// add random lines
for (int i=0; i< numRandomLines; i++) {
points.add(new PVector(random(800), 0)); points.add(new PVector(random(800), height));
}
}
void draw(){
background(255);
beginShape(LINES);
for(PVector point : points) vertex(point.x, point.y);
endShape();
}
void keyReleased() {
if (key == 'r') refresh();
}
and grouping a pair of points (PVector) into a Line class:
int numRandomLines = 4;
ArrayList<Line> lines = new ArrayList<Line>();
void setup() {
size(800, 800);
stroke(0, 150, 255, 150);
strokeWeight(3);
refresh();
}
void refresh(){
// remove previous points
lines.clear();
//add borders
lines.add(new Line(new PVector(0, 0), new PVector(width, 0)));
lines.add(new Line(new PVector(width, 0), new PVector(width - 1, height - 1)));
lines.add(new Line(new PVector(0, height - 1), new PVector(width - 1, height - 1)));
lines.add(new Line(new PVector(0, 0), new PVector(0, height - 1)));
// add random lines
for (int i=0; i< numRandomLines; i++) {
lines.add(new Line(new PVector(random(800), 0), new PVector(random(800), height)));
}
}
void draw(){
background(255);
for(Line line : lines) line.draw();
}
void keyReleased() {
if (key == 'r') refresh();
}
class Line{
PVector start;
PVector end;
Line(PVector start, PVector end){
this.start = start;
this.end = end;
}
void draw(){
line(start.x, start.y, end.x, end.y);
}
}
At this stage to get the individual shapes as your diagram describes, we could cheat and use a computer vision library like OpenCV. This is if course overkill (as we'd get() a PImage copy of the drawing, convert that to an OpenCV image) then simply use findContours() to get each shape/contour.
Going back to the original approach, the line to line intersection function could be integrated into the Line class:
int numRandomLines = 4;
ArrayList<Line> lines = new ArrayList<Line>();
ArrayList<PVector> intersections = new ArrayList<PVector>();
void setup() {
size(800, 800);
strokeWeight(3);
refresh();
}
void refresh(){
// remove previous points
lines.clear();
intersections.clear();
//add borders
lines.add(new Line(new PVector(0, 0), new PVector(width, 0)));
lines.add(new Line(new PVector(width, 0), new PVector(width - 1, height - 1)));
lines.add(new Line(new PVector(0, height - 1), new PVector(width - 1, height - 1)));
lines.add(new Line(new PVector(0, 0), new PVector(0, height - 1)));
// add random lines
for (int i=0; i< numRandomLines; i++) {
lines.add(new Line(new PVector(random(800), 0), new PVector(random(800), height)));
}
// compute intersections
int numLines = lines.size();
// when looping only check if lineA intersects lineB but not also if lineB intersects lineA (redundant)
for (int i = 0; i < numLines - 1; i++){
Line lineA = lines.get(i);
for (int j = i + 1; j < numLines; j++){
Line lineB = lines.get(j);
// check intersection
PVector intersection = lineA.intersect(lineB);
// if there is one, append the intersection point to the list
if(intersection != null){
intersections.add(intersection);
}
}
}
}
void draw(){
background(255);
stroke(0, 150, 255, 150);
// draw lines
for(Line line : lines) line.draw();
stroke(255, 0, 0, 150);
// draw intersections
for(PVector intersection : intersections) ellipse(intersection.x, intersection.y, 9, 9);
}
void keyReleased() {
if (key == 'r') refresh();
}
class Line{
PVector start;
PVector end;
Line(PVector start, PVector end){
this.start = start;
this.end = end;
}
void draw(){
line(start.x, start.y, end.x, end.y);
}
//source: http://jeffreythompson.org/collision-detection/line-line.php
//boolean lineLine(float this.start.x, float this.start.y, float this.end.x, float this.end.y,
//float other.start.x, float other.start.y, float other.end.x, float other.end.y) {
PVector intersect(Line other) {
// calculate the distance to intersection point
float uA = ((other.end.x-other.start.x)*(this.start.y-other.start.y) - (other.end.y-other.start.y)*(this.start.x-other.start.x)) / ((other.end.y-other.start.y)*(this.end.x-this.start.x) - (other.end.x-other.start.x)*(this.end.y-this.start.y));
float uB = ((this.end.x-this.start.x)*(this.start.y-other.start.y) - (this.end.y-this.start.y)*(this.start.x-other.start.x)) / ((other.end.y-other.start.y)*(this.end.x-this.start.x) - (other.end.x-other.start.x)*(this.end.y-this.start.y));
// if uA and uB are between 0-1, lines are colliding
if (uA >= 0 && uA <= 1 && uB >= 0 && uB <= 1) {
// optionally, draw a circle where the lines meet
float intersectionX = this.start.x + (uA * (this.end.x-this.start.x));
float intersectionY = this.start.y + (uA * (this.end.y-this.start.y));
return new PVector(intersectionX, intersectionY);
}
return null;
}
}
The next step would be a more complex algorithm to sort the points based on x, y position (e.g. top to bottom , left to right), iterate though points comparing the first to the rest by distance and angle and trying to work out if consecutive points with minimal distance and angle changes connect.
Having a quick look online I can see such algorithms for example:
Polygon Detection from a Set of Lines
Bentley Ottman algorithm (one of the algorithms mentioned in the paper above) is actually implemented in CGAL. (While there are CGAL Java bindings building these and either interfacing or making a wrapper for Processing isn't trivial).
I can see your code isn't javascript but since you didn't specify a language I assume you just want a method and can convert to your language.
The way I handled this was to assign each line a line number. If I can identify 2 adjacent points on one line then I will know if the third point exist by checking if there is a point at the crossing of the lines they are not sharing.
Example:
There's 3 lines (line 1, 2, 3)
I have an intersection point between lines 3 & 1 now I walk down line 3 for an adjacent point. I find one and its intersection is 3 & 2. Well the only way I could have a triangle is by lines 1 & 2 crossing somewhere. So we can programmatically check that.
Keep in mind that I never actually use and angles for this. I do calculate them in the functions but decided not to use them as I went with the method explained above. I have colored the triangles using an alpha value of 0.1 so you can see where there is overlap.
This is only check triangles
let canvas = document.getElementById("canvas");
let ctx = canvas.getContext("2d");
canvas.width = 400;
canvas.height = 400;
let lines = []; //holds each line
let points = []; //all intersection point are pushed here [{x: num, y: num}, {x: num, y: num},...]
let sortedPts = []; //all points sorted bu first number are pushed here in 2d array.
let lineNum = 15;
class Lines {
constructor(num) {
this.x = Math.round(Math.random() * canvas.width);
this.x2 = Math.round(Math.random() * canvas.width);
this.pt1 = {
x: this.x,
y: 0
};
this.pt2 = {
x: this.x2,
y: canvas.height
};
this.num = num;
this.rads = Math.atan2(this.pt2.y - this.pt1.y, this.pt2.x - this.pt1.x);
this.angle = this.rads * (180 / Math.PI);
}
draw() {
ctx.beginPath();
ctx.moveTo(this.pt1.x, this.pt1.y);
ctx.lineTo(this.pt2.x, this.pt2.y);
ctx.stroke();
}
}
//creates the lines. I also use this function to prepare the 2d array by pushing an empty array for each line into sortedPts.
function createLines() {
for (let i = 0; i < lineNum; i++) {
lines.push(new Lines(i + 1));
sortedPts.push([])
}
}
createLines();
//Visually draws lines on screen
function drawLines() {
for (let i = 0; i < lines.length; i++) {
lines[i].draw();
}
}
drawLines();
//intersecting formula
function lineSegmentsIntersect(line1, line2) {
let a_dx = line1.pt2.x - line1.pt1.x;
let a_dy = line1.pt2.y - line1.pt1.y;
let b_dx = line2.pt2.x - line2.pt1.x;
let b_dy = line2.pt2.y - line2.pt1.y;
let s =
(-a_dy * (line1.pt1.x - line2.pt1.x) + a_dx * (line1.pt1.y - line2.pt1.y)) /
(-b_dx * a_dy + a_dx * b_dy);
let t =
(+b_dx * (line1.pt1.y - line2.pt1.y) - b_dy * (line1.pt1.x - line2.pt1.x)) /
(-b_dx * a_dy + a_dx * b_dy);
if (s >= 0 && s <= 1 && t >= 0 && t <= 1) {
//this is where we create our array but we also add the line number of where each point intersects. I also add the angle but have not used it throughout the rest of this...yet.
points.push({
x: Math.round(line1.pt1.x + t * (line1.pt2.x - line1.pt1.x)),
y: Math.round(line1.pt1.y + t * (line1.pt2.y - line1.pt1.y)),
num: {
first: line1.num,
second: line2.num
},
angle: {
a1: line1.angle,
a2: line2.angle
}
});
}
}
//just checks each line against the others by passing to lineSegmentsIntersect() function
function callIntersect() {
for (let i = 0; i < lines.length; i++) {
for (let j = i + 1; j < lines.length; j++) {
lineSegmentsIntersect(lines[i], lines[j]);
}
}
}
callIntersect();
function drawPoints() {
//just draws the black points for reference
for (let i = 0; i < points.length; i++) {
ctx.beginPath();
ctx.arc(points[i].x, points[i].y, 2, 0, Math.PI * 2);
ctx.fill();
}
}
drawPoints();
function createSortedArray() {
//Now we take the points array and sort the points by the first number to make using i and j below possible
points.sort((a, b) => a.num.first - b.num.first)
//We push each group of points into an array inside sortedPts creating the 2d array
for (let i = 0; i < lineNum; i++) {
for (let j = 0; j < points.length; j++) {
if (points[j].num.first == (i + 1)) {
sortedPts[i].push(points[j]);
}
}
}
//now sort the 2d arrays by y value. This allows or next check to go in order from point to point per line.
sortedPts.forEach(arr => arr.sort((a, b) => a.y - b.y));
fillTriangles();
}
createSortedArray();
/*
The last step iterates through each point in the original points array
and check to see if either the first or second number matches the second
number of a point in our sortedPts array AND do the first or second number
match the next points in the sortedPtsd array. If so then we must have a
triangle.
Quick breakdown. If we have 3 lines (line 1, 2, 3) and I have a points on lines
2 & 3. I also have another point on lines 2 & 1. Then in order to have a triangle
the last point must be on lines 1 & 3.
That's all this is doing.
*/
function fillTriangles() {
//iterate through each array inside sortedPts array
for (let i = 0; i < sortedPts.length; i++) {
//iterate through all points inside each array of points inside the sortedPts array
for (let j = 0; j < sortedPts[i].length - 1; j++) {
//iterate over the original points and compare
for (let k = 0; k < points.length; k++) {
if (
(points[k].num.first == sortedPts[i][j].num.second ||
points[k].num.second == sortedPts[i][j].num.second) &&
(points[k].num.first == sortedPts[i][j + 1].num.second ||
points[k].num.second == sortedPts[i][j + 1].num.second)
) {
ctx.fillStyle = "rgba(200, 100, 0, 0.1)";
ctx.beginPath();
ctx.moveTo(sortedPts[i][j].x, sortedPts[i][j].y);
ctx.lineTo(sortedPts[i][j + 1].x, sortedPts[i][j + 1].y);
ctx.lineTo(points[k].x, points[k].y);
ctx.closePath();
ctx.fill();
}
}
}
}
}
<canvas id="canvas"></canvas>
I also think there's a good way to do this with the angles of the crossing lines and am working on something to do it that way. I am hoping I can get it to determine the type of shape based on the number of sides but I don't see that being a quick project.
Your goal is not clear to me. You can connect any arbitrary set of points in any arbitrary order and call it a shape. What are your criteria?
If you want to find the shortest path that connects all the points of a given subset, I suggest looking for travelling salesman problem.
A couple of days ago I asked a question about translations and rotations in Processing.
I wanted to:
translate, invert and rotate a single quadrilateral (PShape object) multiple times
then change the height of one of its 2 top vertices
so as the whole thing act as an articulated arm that can be bent either to the right or the left.
Thanks to the help of #Rabbid76 I was able to achieve this effect but I am now facing another issue when translating the last 5 top horizontally inverted quads.
When bending the object, the first 3 quads get separated from the last 5 and. And the more the bending leg is curved, the farther they get apart.
I would really appreciate if someone could help me fix the translation part (from line 65 to 68) so as the quads stay attached to each other to matter how strong the bending is.
Any suggestion regarding that matter would be also greatly appreciated.
SCRIPT
int W = 40;
int H = 40;
int nQuads = 8;
int xOffset = 27;
float[] p0 = {-W/2 + xOffset, -H/2};
float[] p1 = {-W/2, H/2};
float[] p2 = {W/2, H/2};
float[] p3 = {W/2, -H/2};
PShape object;
void setup(){
size(600, 600, P2D);
smooth(8);
}
void draw(){
background(255);
// Bending to the left
float bending = sin(frameCount*.05) * .1;
p0[1] -= bending;
pushMatrix();
translate(width/2, height/2);
float minX = min( min(p0[0], p3[0]), min(p2[0], p1[0]) );
float maxX = max( max(p0[0], p3[0]), max(p2[0], p1[0]) );
float cptX = (minX+maxX)/2;
//Rotation Angle
float angle = atan2(p3[1]-p0[1], p3[0]-p0[0]);
//Pivot Height
float PH = p0[1] + (p3[1]-p0[1]) * (cptX-p0[0])/(p3[0]-p0[0]);
for (int i = 0; i < nQuads; i++){
float PivotHeight = (i % 2 == 1) ? PH : H/2;
//Height translation
if (i > 0){
translate(0, PivotHeight);
}
//Rotate once every 2 quads
if (i%2 == 1){
rotate(angle*2);
}
//Height translation
//Flip all quads except 1st one
if (i > 0){
translate(0, PivotHeight);
scale(1, -1);
}
//NOT working --> Flipping horizontally the last 5 top QUADS
if (i == 3){
scale(-1, 1);
translate(- xOffset, 0); //trying to align the quads on the X axis. Y translation is missing
rotate(-angle*2);
}
object();
}
popMatrix();
}
void object() {
beginShape(QUADS);
vertex(p0[0], p0[1]);
vertex(p1[0], p1[1]);
vertex(p2[0], p2[1]);
vertex(p3[0], p3[1]);
endShape();
}
Just providing a workaround to my own question but won't accept it as a valid answer as I don't really understand what I'm doing and it's probably not the most efficient solution.
int W = 40;
int H = 40;
int nQuads = 8;
int xOffset = 27;
float[] p0 = {-W/2 + xOffset, -H/2};
float[] p1 = {-W/2, H/2};
float[] p2 = {W/2, H/2};
float[] p3 = {W/2, -H/2};
PShape object;
void setup(){
size(600, 600, P2D);
smooth(8);
}
void draw(){
background(255);
// Bending to the left
float bending = sin(frameCount*.05) * .3;
p0[1] -= bending;
pushMatrix();
translate(width/2, height/2);
float minX = min( min(p0[0], p3[0]), min(p2[0], p1[0]) );
float maxX = max( max(p0[0], p3[0]), max(p2[0], p1[0]) );
float cptX = (minX+maxX)/2;
//Rotation Angle
float angle = atan2(p3[1]-p0[1], p3[0]-p0[0]);
//Pivot Height
float PH = p0[1] + (p3[1]-p0[1]) * (cptX-p0[0])/(p3[0]-p0[0]);
for (int i = 0; i < nQuads; i++){
float PivotHeight = (i % 2 == 1) ? PH : H/2;
//Height translation
if (i > 0){
translate(0, PivotHeight);
}
//Rotate once every 2 quads
if (i%2 == 1){
rotate(angle*2);
}
//Height translation
//Flip all quads except 1st one
if (i > 0){
translate(0, PivotHeight);
scale(1, -1);
}
//Flipping horizontally the last 5 top QUADS
if (i == 3){
scale(-1, 1);
translate(0, PivotHeight);
rotate(-angle*2);
translate(0, PivotHeight);
translate(-xOffset , H/2 - p0[1]);
}
object();
}
popMatrix();
}
void object() {
beginShape(QUADS);
vertex(p0[0], p0[1]);
vertex(p1[0], p1[1]);
vertex(p2[0], p2[1]);
vertex(p3[0], p3[1]);
endShape();
}
I would like to "mirror" a PShape object like in the picture below:
I know how to display multiple shapes and how to invert them (screenshot below) but things get complicated when I have to rotate them (and probably translating them) so as they "stick" to the preceding shapes (first picture).
I've been trying to compute an angle with the first 2 vertices of the original shape (irregular quadrilateral) and the atan2() function but to no avail.
I would really appreciate if someone could help figuring how to solve this problem.
int W = 20;
int H = 20;
int D = 20;
PShape object;
void setup(){
size(600, 600, P2D);
smooth();
}
void draw(){
background(255);
pushMatrix();
translate(width/2, height/1.3);
int td = -1;
for (int i = 0; i < 6; i++){
translate(0, td*H*2);
scale(-1, 1);
rotate(PI);
object();
td *= -1;
}
popMatrix();
}
void object() {
beginShape(QUADS);
vertex(-20, 20);
vertex(20, 0);
vertex(20, -20);
vertex(-20, -20);
endShape();
}
To do what you want you have to create a shape by 2 given angles for the top and the bottom of the shape angleT and `angleBĀ“. The origin (0,0) is in the center of the shape. This causes that the pivots for the rotations are in the middle of the slopes of the shape :
int W = 40;
int H = 40;
float angleT = -PI/18;
float angleB = PI/15;
PShape object;
void object() {
float H1 = -H/2 + W*tan(angleB);
float H2 = H/2 + W*tan(angleT);
beginShape(QUADS);
vertex(-W/2, -H/2);
vertex(W/2, H1);
vertex(W/2, H2);
vertex(-W/2, H/2);
endShape();
}
When you draw the parts, then you should distinguish between even and odd parts. The parts have to be flipped horizontal by inverting the y axis (scale(1, -1)). The even parts have to be rotated by the double of angleB and the odd parts have to be rotated by the doubled of angleT. For the rotation, the center of the slopes (pivots) have to be translated to the origin:
void setup(){
size(600, 600, P2D);
smooth();
}
void draw(){
background(255);
translate(width/2, height/2);
float HC1 = -H/2 + W*tan(angleB)/2;
float HC2 = H/2 + W*tan(angleT)/2;
for (int i = 0; i < 15; i++){
float angle = (i % 2 == 0) ? -angleB : -angleT;
float HC = (i % 2 == 0) ? HC1 : HC2;
translate(0, -HC);
rotate(angle*2);
translate(0, -HC);
object();
scale(1, -1);
}
}
The algorithm works for any angle, positive and negative including 0.
This algorithm can be further improved. Let's assume you have a quad, defined by 4 points (p0, p1, p2, p3):
float[] p0 = {10, 0};
float[] p1 = {40, 10};
float[] p2 = {60, 45};
float[] p3 = {0, 60};
PShape object;
void object() {
beginShape(QUADS);
vertex(p0[0], p0[1]);
vertex(p1[0], p1[1]);
vertex(p2[0], p2[1]);
vertex(p3[0], p3[1]);
endShape();
}
Calculate the the minimum, maximum, centerpoint, pivots and angles:
float minX = min( min(p0[0], p1[0]), min(p2[0], p3[0]) );
float maxX = max( max(p0[0], p1[0]), max(p2[0], p3[0]) );
float minY = min( min(p0[1], p1[1]), min(p2[1], p3[1]) );
float maxY = max( max(p0[1], p1[1]), max(p2[1], p3[1]) );
float cptX = (minX+maxX)/2;
float cptY = (minY+maxY)/2;
float angleB = atan2(p1[1]-p0[1], p1[0]-p0[0]);
float angleT = atan2(p2[1]-p3[1], p2[0]-p3[0]);
float HC1 = p0[1] + (p1[1]-p0[1])*(cptX-p0[0])/(p1[0]-p0[0]);
float HC2 = p3[1] + (p2[1]-p3[1])*(cptX-p3[0])/(p2[0]-p3[0]);
Draw the shape like before:
for (int i = 0; i < 6; i++){
float angle = (i % 2 == 0) ? -angleB : -angleT;
float HC = (i % 2 == 0) ? HC1 : HC2;
translate(cptX, -HC);
rotate(angle*2);
translate(-cptX, -HC);
object();
scale(1, -1);
}
Another approach would be to stack the shape on both sides:
For this you have to know the heights of the pivots (HC1, HC2) and the angles (angleB, angleT). So this can be implemented based on both of the above approaches.
Define the pivot points and the directions of the top and bottom edge:
PVector dir1 = new PVector(cos(angleB), sin(angleB));
PVector dir2 = new PVector(cos(angleT), sin(angleT));
PVector pv1 = new PVector(0, HC1); // or PVector(cptX, HC1)
PVector pv2 = new PVector(0, HC2); // or PVector(cptX, HC2)
Calculate the intersection point (X) of the both edges. Of course this will work only if the
edges are not parallel:
PVector v12 = pv2.copy().sub(pv1);
PVector nDir = new PVector(dir2.y, -dir2.x);
float d = v12.dot(nDir) / dir1.dot(nDir);
PVector X = pv1.copy().add( dir1.copy().mult(d) );
The stack algorithm works as follows:
for (int i = 0; i < 8; i++){
float fullAngle = angleT-angleB;
float angle = fullAngle * floor(i/2);
if ((i/2) % 2 != 0)
angle += fullAngle;
if (i % 2 != 0)
angle = -angle;
float flip = 1.0;
if (i % 2 != 0)
flip *= -1.0;
if ((i/2) % 2 != 0)
flip *= -1.0;
pushMatrix();
translate(X.x, X.y);
rotate(angle);
scale(1, flip);
rotate(-angleB);
translate(-X.x, -X.y);
object();
popMatrix();
}
I'm trying to do some basic opengl es programming to get started on the basics.
I have a drawing function tries to draw a wedge of a circle. Something is going wrong because its actually just drawing a circle.
I'm still just trying to grasp the basics of opengl es here. Heres what I have so far.
- (void)drawView
{
[EAGLContext setCurrentContext:context];
glBindFramebufferOES(GL_FRAMEBUFFER_OES, viewFramebuffer);
glViewport(0, 0, 60, 60);
int i;
float angle_start=90;
float angle_stop=180;
int segments=360;
float const angle_step = (angle_stop - angle_start)/segments;
GLfloat *arc_vertices;
arc_vertices = malloc(2*sizeof(GLfloat) * (segments+2));
arc_vertices[0] = arc_vertices[1] = 0.0;
for(i=0; i<segments+1; i++) {
arc_vertices[2 + 2*i ] = cos(angle_start + i*angle_step);
arc_vertices[2 + 2*i + 1] = sin(angle_start + i*angle_step);
}
glVertexPointer(2, GL_FLOAT, 0, arc_vertices);
glEnableClientState(GL_VERTEX_ARRAY);
glColor4f(1.0f, 0.0f, 0.0f, 1.0f);
glDrawArrays(GL_TRIANGLE_FAN, 0, segments+2);
glBindRenderbufferOES(GL_RENDERBUFFER_OES, viewRenderbuffer);
[context presentRenderbuffer:GL_RENDERBUFFER_OES];
free(arc_vertices);
}
sin() and cos() take radians as input:
float angle_start=90;
float angle_stop=180;
int segments=360;
float const angle_step = (angle_stop - angle_start)/segments;
GLfloat* verts = (GLfloat*)malloc(2*sizeof(GLfloat) * (segments+2));
unsigned int pos = 0;
verts[pos++] = 0;
verts[pos++] = 0;
float radius = 10;
for( unsigned int i = 0; i < segments; ++i )
{
float rads = (angle_start + i*angle_step) * (3.14159 / 180);
verts[pos++] = ( cos( rads ) * radius );
verts[pos++] = ( sin( rads ) * radius );
}
glVertexPointer(2, GL_FLOAT, 0, verts);
glEnableClientState(GL_VERTEX_ARRAY);
glColor4f(1.0f, 0.0f, 0.0f, 1.0f);
glDrawArrays(GL_TRIANGLE_FAN, 0, segments+1);
glDisableClientState(GL_VERTEX_ARRAY);
I see something wrong. You access vertices[i] and vertices[i+1], but i always increments by 1.
Try replacing
GLfloat vertices[720];
with
GLfloat vertices[2*720];
and replace
vertices[i]=p1;
vertices[i+1]=p2;
by
vertices[2*i]=p1;
vertices[2*i+1]=p2;
this works.
Anti aliasing is horrible but it works.
[credit1
-(void)drawcircelofSlice2
{
amt+=20;
if(amt>360.0)
{
amt=0;
}
[EAGLContext setCurrentContext:context];
glBindFramebufferOES(GL_FRAMEBUFFER_OES, viewFramebuffer);
glViewport(20, 20, 50,50);
glMatrixMode(GL_PROJECTION);
glLoadIdentity();
glOrthof(30.0f, 30.0f, -1.5f, 1.5f, -1.0f, 1.0f);
glMatrixMode(GL_MODELVIEW);
glClearColor(0.0f, 0.0f, 0.0f, 1.0f);
glClear(GL_COLOR_BUFFER_BIT);
float x=0;
float y=0;
//float radius=20;
float lowAngle=0;
float highAngle=(amt/360) *360;
// float highAngle=360;
float numcirclePts=360;
lowAngle=DEGREES_TO_RADIANS(lowAngle);
highAngle=DEGREES_TO_RADIANS(highAngle);
float res=numcirclePts;
float angle=lowAngle;
float anglerange=highAngle-lowAngle;
float angleAdder=anglerange/ res;
int k=0;
GLfloat verts[720];
for (int i = 0; i < numcirclePts; i++){
verts[k] = x + cos(angle) ;
verts[k+1] = y - sin(angle) ;
angle += angleAdder;
k+=2;
}
verts[0] = x;
verts[1] = y;
k = 2;
for (int i = 2; i < numcirclePts; i++){
verts[k] = verts[k];
verts[k+1] = verts[k+1];
k+=2;
}
glVertexPointer(2, GL_FLOAT, 0, verts);
glEnableClientState(GL_VERTEX_ARRAY);
glColor4f(0.0f, 0.0f, 1.0f, 0.0f);
glDrawArrays(GL_TRIANGLE_FAN, 0, numcirclePts);
glBindRenderbufferOES(GL_RENDERBUFFER_OES, viewRenderbuffer);
glDisableClientState(GL_VERTEX_ARRAY);
[context presentRenderbuffer:GL_RENDERBUFFER_OES];
}
I'm trying to draw the following shape using OpenGL ES 1.1. And well, I'm stuck, I don't really know how to go about it.
My game currently uses Android's Canvas API, which isn't hardware accelerated, so I'm rewriting it with OpenGL ES. The Canvas class has a method called drawArc which makes drawing this shape very very easy; Canvas.drawArc
Any advice/hints on doing the same with OpenGL ES?
Thank you for reading.
void gltDrawArc(unsigned int const segments, float angle_start, float angle_stop)
{
int i;
float const angle_step = (angle_stop - angle_start)/segments;
GLfloat *arc_vertices;
arc_vertices = malloc(2*sizeof(GLfloat) * (segments+2));
arc_vertices[0] = arc_vertices[1] = 0.
for(i=0; i<segments+1; i++) {
arc_vertices[2 + 2*i ] = cos(angle_start + i*angle_step);
arc_vertices[2 + 2*i + 1] = sin(angle_start + i*angle_step);
}
glVertexPointer(2, GL_FLOAT, 0, arc_vertices);
glEnableClientState(GL_VERTEX_ARRAY);
glDrawArrays(GL_TRIANGLE_FAN, 0, segments+2);
free(arc_vertices);
}
What about just sampling the circle at discrete angles and drawing a GL_TRIANGLE_FAN?
EDIT: Something like this will just draw a sector of a unit circle around the origin in 2D:
glBegin(GL_TRIANGLE_FAN);
glVertex2f(0.0f, 0.0f);
for(angle=startAngle; angle<=endAngle; ++angle)
glVertex2f(cos(angle), sin(angle));
glEnd();
Actually take this more as pseudocode, as sin and cos usually work on radians and I'm using degrees, but you should get the point.
I am new to android programming so I am sure there is probably a better way to do this. But I was following the OpenGL ES 1.0 tutorial on the android developers site http://developer.android.com/resources/tutorials/opengl/opengl-es10.html which walks you through drawing a green triangle. You can follow the link and you will see most of the code I used there. I wanted to draw a circle on the triangle. The code I added is based on the above example posted by datenwolf. And is shown in snippets below:
public class HelloOpenGLES10Renderer implements GLSurfaceView.Renderer {
// the number small triangles used to make a circle
public int segments = 100;
public float mAngle;
private FloatBuffer triangleVB;
// array to hold the FloatBuffer for the small triangles
private FloatBuffer [] segmentsArray = new FloatBuffer[segments];
private void initShapes(){
.
.
.
// stuff to draw holes in the board
int i = 0;
float angle_start = 0.0f;
float angle_stop = 2.0f * (float) java.lang.Math.PI;
float angle_step = (angle_stop - angle_start)/segments;
for(i=0; i<segments; i++) {
float[] holeCoords;
FloatBuffer holeVB;
holeCoords = new float [ 9 ];
// initialize vertex Buffer for triangle
// (# of coordinate values * 4 bytes per float)
ByteBuffer vbb2 = ByteBuffer.allocateDirect(holeCoords.length * 4);
vbb2.order(ByteOrder.nativeOrder());// use the device hardware's native byte order
holeVB = vbb2.asFloatBuffer(); // create a floating point buffer from the ByteBuffer
float x1 = 0.05f * (float) java.lang.Math.cos(angle_start + i*angle_step);
float y1 = 0.05f * (float) java.lang.Math.sin(angle_start + i*angle_step);
float z1 = 0.1f;
float x2 = 0.05f * (float) java.lang.Math.cos(angle_start + i+1*angle_step);
float y2 = 0.05f * (float) java.lang.Math.sin(angle_start + i+1*angle_step);
float z2 = 0.1f;
holeCoords[0] = 0.0f;
holeCoords[1] = 0.0f;
holeCoords[2] = 0.1f;
holeCoords[3] = x1;
holeCoords[4] = y1;
holeCoords[5] = z1;
holeCoords[6] = x2;
holeCoords[7] = y2;
holeCoords[8] = z2;
holeVB.put(holeCoords); // add the coordinates to the FloatBuffer
holeVB.position(0); // set the buffer to read the first coordinate
segmentsArray[i] = holeVB;
}
}
.
.
.
public void onDrawFrame(GL10 gl) {
.
.
.
// Draw hole
gl.glColor4f( 1.0f - 0.63671875f, 1.0f - 0.76953125f, 1.0f - 0.22265625f, 0.0f);
for ( int i=0; i<segments; i++ ) {
gl.glVertexPointer(3, GL10.GL_FLOAT, 0, segmentsArray[i]);
gl.glDrawArrays(GL10.GL_TRIANGLES, 0, 3);
}
}