Develop Reference

How to determine if two points do not have any obstructions between them

I am currently trying to put together an algorithm where I can know if there is an obstruction between two defined points in a plane.
Here is an example image.
We can see with the image that point 1, 2, 3, & 6 are all accessible from the origin point. Points 4 and 5 are not. You pass through the polygon.
The code I am using is the following. pStartPoint and pEndPoint is the line from the origin to the point in question. The function checks all edges to see if the line passes through the edge.
public double GetSlopeOfLine(Point a, Point b){
double x = b.y - a.y;
double y = b.x - a.x;
return (x / y);
}
public double GetOffsetOfLine(double x, double y, double slope){
return (y - (slope * x));
}
public boolean IsPointAccessable(Point pStartPoint, Point pEndPoint){
//Define the equation of the line for these points. Once we have slope and offset the equation is
//y = slope * x + offset;
double slopeOfLine = GetSlopeOfLine(pStartPoint, pEndPoint);
double offSet = GetOffsetOfLine(pStartPoint.x, pStartPoint.y, slopeOfLine);
//Collision detection for each side of each obstacle. Once we get the point of collision, does it lie on the
//line in between the two points? If so, collision, and I can't reach that point yet.
for (Iterator<Obstacles> ObstacleIt = AdjustedObstaclesList.iterator(); ObstacleIt.hasNext();) {
Obstacles pObstacle = ObstacleIt.next();
int NumberOfEdges = pObstacle.getPoints().size();
for(int i=0; i<NumberOfEdges; i++){
//Get Edge[i];
int index = i;
Point pFirstPoint = (Point)pObstacle.getPoints().get(index);
if(i >= NumberOfEdges - 1)
index = 0;
else
index = i+1;
Point pNextPoint = (Point)pObstacle.getPoints().get(index);
double slopeOfEdge = GetSlopeOfLine(pFirstPoint, pNextPoint);
double offsetEdge = GetOffsetOfLine(pNextPoint.x, pNextPoint.y, slopeOfEdge);
int x = Math.round((float) ((-offSet + offsetEdge) / (slopeOfLine - slopeOfEdge)));
int y = Math.round((float) ((slopeOfLine * x) + offSet));
//If it lies on either point I could be looking at two adjacent points. I can still reach that point.
if(x > pStartPoint.x && x < pEndPoint.x && y > pStartPoint.y && y < pEndPoint.y &&
x > pFirstPoint.x && x < pNextPoint.x && y > pFirstPoint.y && y < pNextPoint.y){
return false;
}
}
}
return true;
}
If the line passes through and the point where the lines cross is found between pStartPoint and pEndPoint I am assuming that pEndPoint cannot be reached.
This function is not working and I am wondering if it has something to do with the fact that the origin is not at the bottom left but at the top left and that (width, height) of my window is located in the bottom right. Therefore the coordinate plane is messed up.
My mind must be mush because I cannot think how to adjust for this and if that is truly my mistake as I cannot seem to fix the error. I thought adjusting the slope and offset by multiplying each by -1 might have been the solution but that doesn't seem to work.
Is my solution the right one? Does my code seem correct in checking for an intersect point? Is there a better solution to see if a point is accessible.
There is also going to be the next step after this where once I determine what points are accessible if I am now on one of the points of the polygon. For example, from point 1 what points are accessible without crossing into the polygon?

First, I would like to say that using slopes for this kind of task is do-able, but also difficult due to the fact that they are very volatile in the sense that they can go from negative infinity to infinity with a very small change in the point. Here's a slightly different algorithm, which relies on angles rather than slopes. Another advantage of using this is that the coordinate systems don't really matter here. It goes like this (I reused as much of your existing code as I could):
public boolean IsPointAccessable(Point pStartPoint, Point pEndPoint) {
//Collision detection for each side of each obstacle. Once we get the point of collision, does it lie on the
//line in between the two points? If so, collision, and I can't reach that point yet.
for (Iterator<Obstacles> ObstacleIt = AdjustedObstaclesList.iterator(); ObstacleIt.hasNext();) {
Obstacles pObstacle = ObstacleIt.next();
int NumberOfEdges = pObstacle.getPoints().size();
for(int i=0; i<NumberOfEdges; i++){
//Get Edge[i];
int index = i;
Point pFirstPoint = (Point)pObstacle.getPoints().get(index);
if(i >= NumberOfEdges - 1)
index = 0;
else
index = i+1;
Point pNextPoint = (Point)pObstacle.getPoints().get(index);
// Here is where we get a bunch of angles that encode in them important info on
// the problem we are trying to solve.
double angleWithStart = getAngle(pNextPoint, pFirstPoint, pStartPoint);
double angleWithEnd = getAngle(pNextPoint, pFirstPoint, pEndPoint);
double angleWithFirst = getAngle(pStartPoint, pEndPoint, pFirstPoint);
double angleWithNext = getAngle(pStartPoint, pEndPoint, pNextPoint);
// We have accumulated all the necessary angles, now we must decide what they mean.
// If the 'start' and 'end' angles are different signs, then the first and next points
// between them. However, for a point to be inaccessible, it also must be the case that
// the 'first' and 'next' angles are opposite sides, as then the start and end points
// Are between them so a blocking occurs. We check for that here using a creative approach
// This is a creative way of checking if two numbers are different signs.
if (angleWithStart * angleWithEnd <= 0 && angleWithFirst * angleWithNext <= 0) {
return false;
}
}
}
return true;
}
Now, all that is left to do is find a method that calculates the signed angle formed by three points. A quick google search yielded this method (from this SO question):
private double getAngle(Point previous, Point center, Point next) {
return Math.toDegrees(Math.atan2(center.x - next.x, center.y - next.y)-
Math.atan2(previous.x- center.x,previous.y- center.y));
}
Now, this method should work in theory (I am testing to be sure and will edit my answer if I find any issues with signs of angles or something like that). I hope you get the idea and that my comments explain the code well enough, but please leave a comment/question if you want me to elaborate further. If you don't understand the algorithm itself, I recommend getting a piece of paper out and following the algorithm to see what exactly is going on. Hope this helps!
EDIT: To hopefully aid in better understanding the solution using angles, I drew a picture with the four base cases of how the start, end, first, and next could be oriented, and have attached it to this question. Sorry for the sloppiness, I drew it rather quickly, but this should in theory make the idea clearer.

If you have a low segment count (for instance, your example only shows 12 segments for three shapes, two shapes of which we know we can ignore (because of bounding box checks), then I would recommend simply performing line/line intersection checking.
Point s = your selected point;
ArrayList<Point> points = polygon.getPoints();
ArrayList<Edge> edges = polygon.getEdges();
for(Point p: points) {
Line l = new Line(s, p);
for(Edge e: edges) {
Point i = e.intersects(l);
if (i != null) {
System.out.println("collision", i.toString());
}
}
}
With an intersects method that is pretty straight forward:
Point intersects(Line l) {
// boring variable aliassing:
double x1 = this.p1.x,
y1 = this.p1.y,
x2 = this.p2.x,
y2 = this.p2.y,
x3 = l.p1.x,
y2 = l.p1.y,
x3 = l.p2.x,
y2 = l.p2.y,
// actual line intersection algebra:
nx = (x1 * y2 - y1 * x2) * (x3 - x4) -
(x1 - x2) * (x3 * y4 - y3 * x4),
ny = (x1 * y2 - y1 * x2) * (y3 - y4) -
(y1 - y2) * (x3 * y4 - y3 * x4),
d = (x1 - x2) * (y3 - y4) - (y1 - y2) * (x3 - x4);
if (d == 0) return null;
return new Point(nx/d, ny/d);
}

processing: trouble using global array in if condition in for loop

I am trying to write a small program that has a given number of balls (in the example code below it's 3) travel back and forth across the screen at different speeds and phases (start offset).
This much has been achieved in the code. Although I want to be able to select the balls (one at a time) using a mouse click.
I have used the word "HIT!!!" to signify in the console that a ball has been clicked.
My problem is that when I run the code below, I only get a "HIT!" in the console when I click the top ball. That is when the first element y[0] matches with the click_Y variable. When I am sure (but obviously mistaken somehow) that there should be matches when I click in the vicinity of y[1] & y[2].
I'd really be grateful for any help with these. As it's gotten to the point where I am starting to stare blankly at the screen. Thanks.
int noCircles; // the number of items in the array (# of circles)
float[] y; // y-position of each circle (fixed)
float[] speed; // speed of each circle
float[] phase; // phase of each circle
float red = 120;
float green = 120;
float blue = 120;
float click_X;
float click_Y;
void setup() {
size(500, 500);
noCircles = 3;
// allocate space for each array
y = new float[noCircles];
speed = new float[noCircles];
phase = new float[noCircles];
// calculate the vertical gap between each circle based on the total number
// of circles
float gap = height / (noCircles + 1);
//setup an initial value for each item in the array
for (int i=0; i<noCircles; i++) {
y[i] = gap * (i + 1);
// y is constant for each so can be calculated once
speed[i] = random(10);
phase[i] = random(TWO_PI);
}
}
void draw() {
background(155);
for (int i=0; i<noCircles; i++) {
// calculate the x-position of each ball based on the speed, phase and
//current frame
float x = width/2 + sin(radians(frameCount*speed[i] ) + phase[i])* 200;
if (dist(x, y[i], click_X, click_Y) <= 20){
println("HIT!!!!!!!!!!!!!!!!!!");
}
ellipse(x, y[i], 20, 20);
click_X = 0;
click_Y = 0;
}
}
void mousePressed() {
println("You clicked******************************************");
click_X = mouseX;
click_Y = mouseY;
println("click_X =" + click_X);
println("click_Y =" + click_Y);
}

Problems like these are best solved by debugging your program. Start by tracing through the code by hand, then add print statements (more than you've already added), and if that doesn't work then don't be afraid to use the debugger.
You're using the click_X and click_Y variables to check the position of the mouse against the position of each ball. Trace through the for loop in your draw() function. What happens at the end of the first iteration?
You reset the values of click_X and click_Y. That's why you aren't detecting any hits on the other circles.
You could probably refactor your code to only reset those variables if something has been hit, but really, I would stop using them altogether.
I'm guessing that you're using those variables because you only want to check when the mouse is pressed? Just use the mousePressed variable for that. Then you can use the mouseX and mouseY variables directly.
Then your if statement would look like this:
if (mousePressed && dist(x, y[i], mouseX, mouseY) <= 20) {
println("HIT: " + i);
}
Also, using separate arrays like this is called parallel arrays, and is general a bad habit to get into. You should probably use classes instead.

Make a rectangle move to point B one pixel at a time in a strait line

I have a rectangle which when I hold down the mouse button I want that rectangle to move to that point following a strait line 1 pixel at a time.
This is my code so far (I put comments in it so you can understand)
float distanceX = finalX - x; //the number of pixels needed to get to destination on the X axis
float distanceY = finalY - y; // same as above but Y axis
float moveX = distanceX > 0 ? 1 : -1; // I only want it to move 1 pixel per render
float moveY = distanceY > 0 ? 1 : -1; // same as above
Array<Stuff> collidedX = new Array<Stuff>(); //saves collisions seperately for x and y
Array<Stuff> collidedY = new Array<Stuff>(); //because I want the square to move where the mouse is pointing even if it means only aligning one axis
for (Stuff s : collidables) {
if (overlapsT(s, x + moveX, y)) {
collidedX.add(s);
}
}
if (collidedX.size < 1) {
if (distanceX != 0)
x += moveX;
}
for (Stuff s : collidables) {
if (overlapsT(s, x, y + moveY)) {
collidedY.add(s);
}
}
if (collidedY.size < 1) {
if (distanceY != 0)
y += moveY;
}
right now the problem is it goes perfectly diagonal until it lines up with one of the axis and then moves up down left or right to the destination.
I don't want to move fractions of pixels. The way my custom physics engine works is each pixel matters, fractional pixels are no good so I am trying to figure out how to smooth the path or rather how to decide when to add 1 to x and then y.

Currently I can't comment, so I have to answer. I think the Bresenham's line algorithm will help you out. It's for drawing rasterize lines.
Bresenham

Creating a circle out of tiles

This is my first attempt at creating a 2D game, so my code probably isn't as efficient as it could be. Anyway, I tried creating a method to create circles out of my tiles. The point of this method is to create circular dirt patches across my screen. Here is a bit of my code:
private void generateDirt(int x, int y) {
int dirt = 3;
int radius = random.nextInt(7) + 3;
for (int i = radius; i > 1; i--) {
for (int angle = 0; angle < 360; angle++) {
double theta = Math.toRadians(angle);
// Broken Line to solve jutting blocks
// if (theta % Math.PI == 0) theta = 0;
tiles[(int) (x + radius * (Math.sin(theta) * Math.cos(theta)))
+ (int) (y + radius
* (Math.sin(theta) * Math.sin(theta))) * width] = dirt;
}
radius--;
}
}
If I comment out the part where I decrease the radius, and draw just a single circle outline (comment out the outermost for loop(int i = radius...) then the circle is drawn perfectly, except for these two strange tiles jutting out in the side. Sometimes the jutting block is on the right side (I thought it was when it was equal to pi / 2) and on the bottom side as well. But the main problem is that when I attempt to fill the circle by decreasing the radius, the circle...well... becomes a square. It loses its round shape and develops very rigid corners.
I worked on this pretty late, I'm not even sure if my math is correct. TBH, I just kinda threw in the trig functions at random and finally got something that looked like a circle. If you can help me identify what is wrong, or tell me a better way to do this, please let me know! Thanks for the help!
*Also, the radius is actually the diameter (I counted), I need to change the name...

Well I found the answer to my own question. It turns out I don't need to convert my angles to radians. In fact, that just messes up the coordinates. Just using the "angle" instead of "theta" variable fixes the problem.

A fast collision detection between a circle and a sprite in pixel perfect

I've been thinking on some fast and brilliant pixel - perfect collision detection between a circle and any sprite. I need to get 2 points of collision to be able to calculate a normal vector out of them later. I managed to come up with some solution but the more scaling is done in my game, the more inaccurate and unprecise this collision is...It seems as if the code I posted below, was good and correct becouse I have been checking it already a few times and spent a few days reading it again and again... I also checked visually that the collision masks and areas of collision are calculated perfectly fine in the code below so the problem definitely doesn't lay there but in this method.
So I guess that the problem here is the loss of data in floating point arithmetic unless somebody finds a flaw in this method?
If however the problem is really with the float loss of data, what other solution would you recommend to find 2 points of collision between circle and any other sprite in pixel perfect? I really liked my solution becouse it was relatively fast
int xOffset1 = (int)colRectLeft; // left boundary of the collision area for the first sprite
int xOffset2 = (int)colCircleLeft; // left boundary of the collision area for the circle sprite
int yOffset1 = (int)colRectBottom; // bottom boundary of the collision area for the first sprite
int yOffset2 = (int)colCircleBottom; // bottom boundary of the collision area for the circle sprite
int width = (int)(colCircleRight - colCircleLeft); //width of the collision area - same for both sprites
int height = (int)(colCircleTop - colCircleBottom); // height of the collision area same for both sprites
// Pixel-perfect COLLISION DETECTION between circle and a sprite
// my custom vector classes - nothing special
Math2D.Vector_2 colRightPoint = new Math2D.Vector_2(-1, -1); // The right point of collision lying on the circle's circumference
Math2D.Vector_2 colLeftPoint = new Math2D.Vector_2(-1, -1); // the left point of collision lying on the circle's circumference
boolean colRightFound = false;
boolean colLeftFound = false;
// I'm going through y in the circle's area of collision
for (float y = yOffset2; y < yOffset2 + height; y += 1)
{
// from equation: (x-Sx)^2 + (y-Sy)^2 = r^2
// x1/2 = (+-)sqrt(r^2 - (y - Sy)^2) + Sx
//(Sx, Sy) is (circle's radius, circle's radius) becouse I want the points on the circle's circumference to have positive coordinates
float x1 = (float) (Math.sqrt(radius*radius - (y - radius)*(y - radius)) + radius); // the right pixel on the circumference
float x2 = (float) (-x1 + 2*radius); // the left pixel on the circumference
//first I check if the calculated x is inside of the previously calculated area of collision for both circle's area and a sprite's area
if (x1 >= xOffset2 &&
x1 <= xOffset2 + width &&
xOffset1 + x1 - xOffset2 < rectFrameW &&
yOffset1 + (int)y-yOffset2 < rectFrameH &&
yOffset1 + (int)y-yOffset2 > 0 &&
xOffset1 + x1 - xOffset2 > 0)
{
//I don't have to check if the point on the circle's circumference is opaque becouse it's always so just check if the same point translated to sprite's area of collision is opaque
boolean opaqueRectPixel = go.gameData.images.get(go.pic_nr)
.collision_mask[(int)((yOffset1 + (int)y-yOffset2)*rectFrameW +
(xOffset1 + x1 - xOffset2))];
if(opaqueRectPixel)
{
if(!colRightFound)
{
colRightPoint.x = (xOffset1 + x1 - xOffset2);
colRightPoint.y = (yOffset1 + (int)y - yOffset2);
colRightFound = true;
}
else if(!colLeftFound)
{
colLeftPoint.x = (xOffset1 + x1 - xOffset2);
colLeftPoint.y = (yOffset1 + (int)y - yOffset2);
}
}
}
//the same logic for the left point on the circle's circumference
if (x2 >= xOffset2 &&
x2 <= xOffset2 + width &&
xOffset1 + x2 - xOffset2 < rectFrameW &&
yOffset1 + (int)y-yOffset2 < rectFrameH &&
yOffset1 + (int)y-yOffset2 > 0 &&
xOffset1 + x2 - xOffset2 > 0)
{
boolean opaqueRectPixel = go.gameData.images.get(go.pic_nr)
.collision_mask[(int)((yOffset1 + (int)y-yOffset2)*rectFrameW +
(xOffset1 + x2 - xOffset2))];
if(opaqueRectPixel)
{
if(!colLeftFound)
{
colLeftPoint.x = (xOffset1 + x2 - xOffset2);
colLeftPoint.y = (yOffset1 + (int)y - yOffset2);
colLeftFound = true;
}
else if(!colRightFound)
{
colRightPoint.x = (xOffset1 + x2 - xOffset2);
colRightPoint.y = (yOffset1 + (int)y - yOffset2);
}
}
}
// if both points are already found, finish
if(colLeftFound && colRightFound)
break;
}
edit: Actually, what I'm doing in this method is finding points of intersection between circle and a sprite
edit: Ok, I'm uploading images to describe my algorithm a bit better. I really tried my best to explain it but if there's still something missing, let me know please!
Also I would accept any other good solutions to find intersection points between a circle and any sprite in pixel perfect, if you don't want to check my code :(... Eh, I'm always having problems with collisions...

If you absolutely want (or need) pixel perfect, your solution looks good.
don't forget to first make a rectangle-to-rectangle collision before testing a pixel perfect detection, to avoid unneeded processings.
If you want another accurate method which maybe more efficient, look for Separating Axis Theorem.
You can find more information about it here :
http://rocketmandevelopment.com/blog/separation-of-axis-theorem-for-collision-detection/
and here :
http://www.metanetsoftware.com/technique/tutorialA.html
The last one have nice interactive explanation and demonstration. Enjoy :)

...as I was not able to show the raster in the comments:
I did not mentally parse your code, however from the image I see that you try to detect borderline collisions. Putting round or diagonal (border)lines into a raster may cause occasions, where two crossing lines do not overlay each other - like this:
1 2
2 1
whereby 1 would be line 1 and 2 would be line 2.
However I still like the idea of checking border lines combined with rectangle pre-checks. If you would render an array of raster proved-closed line coordinates by sprites you could check them against each other. This could also be enriched by border line segmenting (such as North, East, West and South or a bit more fine grain - I guess there is an optimum). A diagonal proved-closed line in the check data set must represent something like this:
x _
x x
whereby the x represent the pixels of your line and the _ is an empty raster seat.