Point in Polygon Algorithm - c

I saw the below algorithm works to check if a point is in a given polygon from this link:
int pnpoly(int nvert, float *vertx, float *verty, float testx, float testy)
{
int i, j, c = 0;
for (i = 0, j = nvert-1; i < nvert; j = i++) {
if ( ((verty[i]>testy) != (verty[j]>testy)) &&
(testx < (vertx[j]-vertx[i]) * (testy-verty[i]) / (verty[j]-verty[i]) + vertx[i]) )
c = !c;
}
return c;
}
I tried this algorithm and it actually works just perfect. But sadly I cannot understand it well after spending some time trying to get the idea of it.
So if someone is able to understand this algorithm, please explain it to me a little.
Thank you.

The algorithm is ray-casting to the right. Each iteration of the loop, the test point is checked against one of the polygon's edges. The first line of the if-test succeeds if the point's y-coord is within the edge's scope. The second line checks whether the test point is to the left of the line (I think - I haven't got any scrap paper to hand to check). If that is true the line drawn rightwards from the test point crosses that edge.
By repeatedly inverting the value of c, the algorithm counts how many times the rightward line crosses the polygon. If it crosses an odd number of times, then the point is inside; if an even number, the point is outside.
I would have concerns with a) the accuracy of floating-point arithmetic, and b) the effects of having a horizontal edge, or a test point with the same y-coord as a vertex, though.

Edit 1/30/2022: I wrote this answer 9 years ago when I was in college. People in the chat conversation are indicating it's not accurate. You should probably look elsewhere. 🤷‍♂️
Chowlett is correct in every way, shape, and form.
The algorithm assumes that if your point is on the line of the polygon, then that is outside - for some cases, this is false. Changing the two '>' operators to '>=' and changing '<' to '<=' will fix that.
bool PointInPolygon(Point point, Polygon polygon) {
vector<Point> points = polygon.getPoints();
int i, j, nvert = points.size();
bool c = false;
for(i = 0, j = nvert - 1; i < nvert; j = i++) {
if( ( (points[i].y >= point.y ) != (points[j].y >= point.y) ) &&
(point.x <= (points[j].x - points[i].x) * (point.y - points[i].y) / (points[j].y - points[i].y) + points[i].x)
)
c = !c;
}
return c;
}

I changed the original code to make it a little more readable (also this uses Eigen). The algorithm is identical.
// This uses the ray-casting algorithm to decide whether the point is inside
// the given polygon. See https://en.wikipedia.org/wiki/Point_in_polygon#Ray_casting_algorithm
bool pnpoly(const Eigen::MatrixX2d &poly, float x, float y)
{
// If we never cross any lines we're inside.
bool inside = false;
// Loop through all the edges.
for (int i = 0; i < poly.rows(); ++i)
{
// i is the index of the first vertex, j is the next one.
// The original code uses a too-clever trick for this.
int j = (i + 1) % poly.rows();
// The vertices of the edge we are checking.
double xp0 = poly(i, 0);
double yp0 = poly(i, 1);
double xp1 = poly(j, 0);
double yp1 = poly(j, 1);
// Check whether the edge intersects a line from (-inf,y) to (x,y).
// First check if the line crosses the horizontal line at y in either direction.
if ((yp0 <= y) && (yp1 > y) || (yp1 <= y) && (yp0 > y))
{
// If so, get the point where it crosses that line. This is a simple solution
// to a linear equation. Note that we can't get a division by zero here -
// if yp1 == yp0 then the above if will be false.
double cross = (xp1 - xp0) * (y - yp0) / (yp1 - yp0) + xp0;
// Finally check if it crosses to the left of our test point. You could equally
// do right and it should give the same result.
if (cross < x)
inside = !inside;
}
}
return inside;
}
To expand on the "too-clever trick". We want to iterate over all adjacent vertices, like this (imagine there are 4 vertices):
i
j
0
1
1
2
2
3
3
0
My code above does it the simple obvious way - j = (i + 1) % num_vertices. However this uses integer division which is much much slower than all other operations. So if this is performance critical (e.g. in an AAA game) you want to avoid it.
The original code changes the order of iteration a bit:
i
j
0
3
1
0
2
1
3
2
This is still totally valid since we're still iterating over every vertex pair and it doesn't really matter whether you go clockwise or anticlockwise, or where you start. However now it lets us avoid the integer division. In easy-to-understand form:
int i = 0;
int j = num_vertices - 1; // 3
while (i < num_vertices) { // 4
{body}
j = i;
++i;
}
Or in very terse C style:
for (int i = 0, j = num_vertices - 1; i < num_vertices; j = i++) {
{body}
}

This might be as detailed as it might get for explaining the ray-tracing algorithm in actual code. It might not be optimized but that must always come after a complete grasp of the system.
//method to check if a Coordinate is located in a polygon
public boolean checkIsInPolygon(ArrayList<Coordinate> poly){
//this method uses the ray tracing algorithm to determine if the point is in the polygon
int nPoints=poly.size();
int j=-999;
int i=-999;
boolean locatedInPolygon=false;
for(i=0;i<(nPoints);i++){
//repeat loop for all sets of points
if(i==(nPoints-1)){
//if i is the last vertex, let j be the first vertex
j= 0;
}else{
//for all-else, let j=(i+1)th vertex
j=i+1;
}
float vertY_i= (float)poly.get(i).getY();
float vertX_i= (float)poly.get(i).getX();
float vertY_j= (float)poly.get(j).getY();
float vertX_j= (float)poly.get(j).getX();
float testX = (float)this.getX();
float testY = (float)this.getY();
// following statement checks if testPoint.Y is below Y-coord of i-th vertex
boolean belowLowY=vertY_i>testY;
// following statement checks if testPoint.Y is below Y-coord of i+1-th vertex
boolean belowHighY=vertY_j>testY;
/* following statement is true if testPoint.Y satisfies either (only one is possible)
-->(i).Y < testPoint.Y < (i+1).Y OR
-->(i).Y > testPoint.Y > (i+1).Y
(Note)
Both of the conditions indicate that a point is located within the edges of the Y-th coordinate
of the (i)-th and the (i+1)- th vertices of the polygon. If neither of the above
conditions is satisfied, then it is assured that a semi-infinite horizontal line draw
to the right from the testpoint will NOT cross the line that connects vertices i and i+1
of the polygon
*/
boolean withinYsEdges= belowLowY != belowHighY;
if( withinYsEdges){
// this is the slope of the line that connects vertices i and i+1 of the polygon
float slopeOfLine = ( vertX_j-vertX_i )/ (vertY_j-vertY_i) ;
// this looks up the x-coord of a point lying on the above line, given its y-coord
float pointOnLine = ( slopeOfLine* (testY - vertY_i) )+vertX_i;
//checks to see if x-coord of testPoint is smaller than the point on the line with the same y-coord
boolean isLeftToLine= testX < pointOnLine;
if(isLeftToLine){
//this statement changes true to false (and vice-versa)
locatedInPolygon= !locatedInPolygon;
}//end if (isLeftToLine)
}//end if (withinYsEdges
}
return locatedInPolygon;
}
Just one word about optimization: It isn't true that the shortest (and/or the tersest) code is the fastest implemented. It is a much faster process to read and store an element from an array and use it (possibly) many times within the execution of the block of code than to access the array each time it is required. This is especially significant if the array is extremely large. In my opinion, by storing each term of an array in a well-named variable, it is also easier to assess its purpose and thus form a much more readable code. Just my two cents...

The algorithm is stripped down to the most necessary elements. After it was developed and tested all unnecessary stuff has been removed. As result you can't undertand it easily but it does the job and also in very good performance.
I took the liberty to translate it to ActionScript-3:
// not optimized yet (nvert could be left out)
public static function pnpoly(nvert: int, vertx: Array, verty: Array, x: Number, y: Number): Boolean
{
var i: int, j: int;
var c: Boolean = false;
for (i = 0, j = nvert - 1; i < nvert; j = i++)
{
if (((verty[i] > y) != (verty[j] > y)) && (x < (vertx[j] - vertx[i]) * (y - verty[i]) / (verty[j] - verty[i]) + vertx[i]))
c = !c;
}
return c;
}

This algorithm works in any closed polygon as long as the polygon's sides don't cross. Triangle, pentagon, square, even a very curvy piecewise-linear rubber band that doesn't cross itself.
1) Define your polygon as a directed group of vectors. By this it is meant that every side of the polygon is described by a vector that goes from vertex an to vertex an+1. The vectors are so directed so that the head of one touches the tail of the next until the last vector touches the tail of the first.
2) Select the point to test inside or outside of the polygon.
3) For each vector Vn along the perimeter of the polygon find vector Dn that starts on the test point and ends at the tail of Vn. Calculate the vector Cn defined as DnXVn/DN*VN (X indicates cross product; * indicates dot product). Call the magnitude of Cn by the name Mn.
4) Add all Mn and call this quantity K.
5) If K is zero, the point is outside the polygon.
6) If K is not zero, the point is inside the polygon.
Theoretically, a point lying ON the edge of the polygon will produce an undefined result.
The geometrical meaning of K is the total angle that the flea sitting on our test point "saw" the ant walking at the edge of the polygon walk to the left minus the angle walked to the right. In a closed circuit, the ant ends where it started.
Outside of the polygon, regardless of location, the answer is zero.
Inside of the polygon, regardless of location, the answer is "one time around the point".

This method check whether the ray from the point (testx, testy) to O (0,0) cut the sides of the polygon or not .
There's a well-known conclusion here: if a ray from 1 point and cut the sides of a polygon for a odd time, that point will belong to the polygon, otherwise that point will be outside the polygon.

To expand on #chowlette's answer where the second line checks if the point is to the left of the line,
No derivation is given but this is what I worked out:
First it helps to imagine 2 basic cases:
the point is left of the line . / or
the point is right of the line / .
If our point were to shoot a ray out horizontally where would it strike the line segment. Is our point to the left or right of it? Inside or out? We know its y coordinate because it's by definition the same as the point. What would the x coordinate be?
Take your traditional line formula y = mx + b. m is the rise over the run. Here, instead we are trying to find the x coordinate of the point on that line segment that has the same height (y) as our point.
So we solve for x: x = (y - b)/m. m is rise over run, so this becomes run over rise or (yj - yi)/(xj - xi) becomes (xj - xi)/(yj - yi). b is the offset from origin. If we assume yi as the base for our coordinate system, b becomes yi. Our point testy is our input, subtracting yi turns the whole formula into an offset from yi.
We now have (xj - xi)/(yj - yi) or 1/m times y or (testy - yi): (xj - xi)(testy - yi)/(yj - yi) but testx isn't based to yi so we add it back in order to compare the two ( or zero testx as well )

I think the basic idea is to calculate vectors from the point, one per edge of the polygon. If vector crosses one edge, then the point is within the polygon. By concave polygons if it crosses an odd number of edges it is inside as well (disclaimer: although not sure if it works for all concave polygons).

This is the algorithm I use, but I added a bit of preprocessing trickery to speed it up. My polygons have ~1000 edges and they don't change, but I need to look up whether the cursor is inside one on every mouse move.
I basically split the height of the bounding rectangle to equal length intervals and for each of these intervals I compile the list of edges that lie within/intersect with it.
When I need to look up a point, I can calculate - in O(1) time - which interval it is in and then I only need to test those edges that are in the interval's list.
I used 256 intervals and this reduced the number of edges I need to test to 2-10 instead of ~1000.

Here's a php implementation of this:
<?php
class Point2D {
public $x;
public $y;
function __construct($x, $y) {
$this->x = $x;
$this->y = $y;
}
function x() {
return $this->x;
}
function y() {
return $this->y;
}
}
class Point {
protected $vertices;
function __construct($vertices) {
$this->vertices = $vertices;
}
//Determines if the specified point is within the polygon.
function pointInPolygon($point) {
/* #var $point Point2D */
$poly_vertices = $this->vertices;
$num_of_vertices = count($poly_vertices);
$edge_error = 1.192092896e-07;
$r = false;
for ($i = 0, $j = $num_of_vertices - 1; $i < $num_of_vertices; $j = $i++) {
/* #var $current_vertex_i Point2D */
/* #var $current_vertex_j Point2D */
$current_vertex_i = $poly_vertices[$i];
$current_vertex_j = $poly_vertices[$j];
if (abs($current_vertex_i->y - $current_vertex_j->y) <= $edge_error && abs($current_vertex_j->y - $point->y) <= $edge_error && ($current_vertex_i->x >= $point->x) != ($current_vertex_j->x >= $point->x)) {
return true;
}
if ($current_vertex_i->y > $point->y != $current_vertex_j->y > $point->y) {
$c = ($current_vertex_j->x - $current_vertex_i->x) * ($point->y - $current_vertex_i->y) / ($current_vertex_j->y - $current_vertex_i->y) + $current_vertex_i->x;
if (abs($point->x - $c) <= $edge_error) {
return true;
}
if ($point->x < $c) {
$r = !$r;
}
}
}
return $r;
}
Test Run:
<?php
$vertices = array();
array_push($vertices, new Point2D(120, 40));
array_push($vertices, new Point2D(260, 40));
array_push($vertices, new Point2D(45, 170));
array_push($vertices, new Point2D(335, 170));
array_push($vertices, new Point2D(120, 300));
array_push($vertices, new Point2D(260, 300));
$Point = new Point($vertices);
$point_to_find = new Point2D(190, 170);
$isPointInPolygon = $Point->pointInPolygon($point_to_find);
echo $isPointInPolygon;
var_dump($isPointInPolygon);

I modified the code to check whether the point is in a polygon, including the point is on an edge.
bool point_in_polygon_check_edge(const vec<double, 2>& v, vec<double, 2> polygon[], int point_count, double edge_error = 1.192092896e-07f)
{
const static int x = 0;
const static int y = 1;
int i, j;
bool r = false;
for (i = 0, j = point_count - 1; i < point_count; j = i++)
{
const vec<double, 2>& pi = polygon[i);
const vec<double, 2>& pj = polygon[j];
if (fabs(pi[y] - pj[y]) <= edge_error && fabs(pj[y] - v[y]) <= edge_error && (pi[x] >= v[x]) != (pj[x] >= v[x]))
{
return true;
}
if ((pi[y] > v[y]) != (pj[y] > v[y]))
{
double c = (pj[x] - pi[x]) * (v[y] - pi[y]) / (pj[y] - pi[y]) + pi[x];
if (fabs(v[x] - c) <= edge_error)
{
return true;
}
if (v[x] < c)
{
r = !r;
}
}
}
return r;
}

Related

display 2 options side by side from array in gamemaker?

Recently I purchased gamemaker and followed Shaun Spalding's menu tutorial to get set up, but I've come across something that I want to change with the code. In the tutorial the options from the array are positioned so that they are one above the other, however for my game I want them to be right next to each other so that option 1 can be positioned on the left side of the screen, and option 2 on the right side of the screen on the same 'line' (but still able to switch between selecting either).
This is what it looks like currently.
As you can see, they are above each other, when really I want them side by side.
This is the code I have:
'Create' Event:
instruction[0] = "Back";
instruction[1] = "Start Game";
space = 100;
ipos = 0;
'Step' Event:
var move = 0;
move -= max(keyboard_check_pressed(vk_left),keyboard_check_pressed(ord("A")),0);
move += max(keyboard_check_pressed(vk_right),keyboard_check_pressed(ord("D")),0);
if (move != 0)
{
ipos += move;
if (ipos < 0) ipos = array_length_1d(instruction) - 1;
if (ipos > array_length_1d(instruction) - 1) ipos = 0;
}
var push;
push = max(keyboard_check_released(vk_enter),keyboard_check_released(vk_shift),keyboard_check_released(vk_space),0);
if (push == 1) scr_instructions();
'Draw' Event:
draw_set_halign(fa_left);
draw_set_valign(fa_middle);
draw_set_font(fnt_options);
draw_set_color(c_white);
var m;
for (m = 0; m < array_length_1d(instruction); m += 1)
{
draw_text(x + space, y + (m * space),string(instruction[m]))
}
draw_sprite(sprite_index, -1, x + 16, y + ipos * space - 21);
Anyone know what I need to change to get this to work?
Your draw_text seems to increase the y coordinate for each iteration in the loop.
Try to increase x using m instead.
Example:
draw_text(x + (m * space), y + space,string(instruction[m]))
You will likely have to adapt the spacing to get desired look.
Easiest is probably to hard code the coordinates instead of using a loop.
Do the same with draw_sprite.
draw_sprite(sprite_index, -1, x + 16 + ipos * space, y - 21);

Taking an array option out for one cycle

Ok so I have this code where spawn locations are put into an array and then one of the locations is picked at random with this code:
let randx = spawnLocations[Int(arc4random_uniform(UInt32(spawnLocations.count)))]
obstacle.position = CGPoint(x: randx, y: 0)
Object Spawning code:
var spawnLocations:[CGFloat] = []
func getObjectSpawnLocation() {
//Create 5 possible spawn locations
let numberOfNodes = 5
// Spacing between nodes will change if: 1) number of nodes is changed, 2) screen width is changed, 3) node's size is changed.
for i in 0...numberOfNodes - 1 {
// spacing used to space out the nodes according to frame (which changes with screen width)
var xPosition = (frame.maxX /*- thePlayer.size.width*/) / CGFloat((numberOfNodes - 1)) * CGFloat(i)
//add a half of a player's width because node's anchor point is (0.5, 0.5) by default
xPosition += thePlayer.size.width/2
//I have no idea what this does but it works.
xPosition -= frame.maxX/1.6
spawnLocations.append( xPosition )
}
()
}
But I have a problem because sometimes the game spawns the objects like in the picture below and it does not let my player advance any further without them dying and so my question is:
Is there anyway I can stop it from doing this?
maybe take one of the spawning locations out of the array temporally?
I should also note that each of the objects (Skulls) are spawned one after the other not all at once and the skulls can spawn at any of the 5 horizontal locations.
The player can only be trapped between the skulls and the screen's edge. You should keep track whether or not you are currently "wedging" the player in or not, for example:
//Keep instance variables to track your current state
BOOL lineFromEdge; //YES if you're currently drawing a "line" of skulls from an edge
BOOL leftEdge; //YES if the line originates from the left edge, NO if from the right
int previousIndex;
Then you determine the value as follows:
- (int) randomIndex {
int randIndex = Int(arc4random_uniform(UInt32(spawnLocations.count)));
// This expression tells you if your current index is at an edge
if (randIndex == 0 || randIndex == (spawnLocations.count - 1)) {
lineFromEdge = YES;
leftEdge = randIndex == 0;
}
//Check if you left a gap
BOOL didLeaveGap = abs(randIndex - previousIndex) > 1
if (didLeaveGap) lineFromEdge = NO;
if ((lineFromEdge && leftEdge && randomIndex == spawnLocations.count) ||
(lineFromEdge && !leftEdge && randomIndex == 0)) {
//You have drawn a line from one edge to the other without leaving a gap;
//Calculate another index and perform the same checks again
return [self randomIndex];
}
//Your index is valid
previousIndex = randIndex;
return randIndex;
}
Note: Your algorithm must return 0 or spawnLocations.count as very first index for this to work. Else your skulls may start at the center and still wedge the player in without you realizing it.

Given an array, find combinations of n numbers that are less than c

This is a tough one, at least for my minimal c skills.
Basically, the user enters a list of prices into an array, and then the desired number of items he wants to purchase, and finally a maximum cost not to exceed.
I need to check how many combinations of the desired number of items are less than or equal to the cost given.
If the problem was a fixed number of items in the combination, say 3, it would be much easier with just three loops selecting each price and adding them to test.
Where I get stumped is the requirement that the user enter any number of items, up to the number of items in the array.
This is what I decided on at first, before realizing that the user could specify combinations of any number, not just three. It was created with help from a similar topic on here, but again it only works if the user specifies he wants 3 items per combination. Otherwise it doesn't work.
// test if any combinations of items can be made
for (one = 0; one < (count-2); one++) // count -2 to account for the two other variables
{
for (two = one + 1; two < (count-1); two++) // count -1 to account for the last variable
{
for (three = two + 1; three < count; three++)
{
total = itemCosts[one] + itemCosts[two] + itemCosts[three];
if (total <= funds)
{
// DEBUG printf("\nMatch found! %d + %d + %d, total: %d.", itemCosts[one], itemCosts[two], itemCosts[three], total);
combos++;
}
}
}
}
As far as I can tell there's no easy way to adapt this to be flexible based on the user's desired number of items per combination.
I would really appreciate any help given.
One trick to flattening nested iterations is to use recursion.
Make a function that takes an array of items that you have selected so far, and the number of items you've picked up to this point. The algorithm should go like this:
If you have picked the number of items equal to your target of N, compute the sum and check it against the limit
If you have not picked enough items, add one more item to your list, and make a recursive call.
To ensure that you do not pick the same item twice, pass the smallest index from which the function may pick. The declaration of the function may look like this:
int count_combinations(
int itemCosts[]
, size_t costCount
, int pickedItems[]
, size_t pickedCount
, size_t pickedTargetCount
, size_t minIndex
, int funds
) {
if (pickedCount == pickedTargetCount) {
// This is the base case. It has the code similar to
// the "if" statement from your code, but the number of items
// is not fixed.
int sum = 0;
for (size_t i = 0 ; i != pickedCount ; i++) {
sum += pickedItems[i];
}
// The following line will return 0 or 1,
// depending on the result of the comparison.
return sum <= funds;
} else {
// This is the recursive case. It is similar to one of your "for"
// loops, but instead of setting "one", "two", or "three"
// it sets pickedItems[0], pickedItems[1], etc.
int res = 0;
for (size_t i = minIndex ; i != costCount ; i++) {
pickedItems[pickedCount] = itemCosts[i];
res += count_combinations(
itemCosts
, costCount
, pickedItems
, pickedCount+1
, pickedTargetCount
, i+1
, funds
);
}
return res;
}
}
You call this function like this:
int itemCosts[C] = {...}; // The costs
int pickedItems[N]; // No need to initialize this array
int res = count_combinations(itemCosts, C, pickedItems, 0, N, 0, funds);
Demo.
This can be done by using a backtracking algorithm. This is equivalent to implementing a list of nested for loops. This can be better understood by trying to see the execution pattern of a sequence of nested for loops.
For example lets say you have, as you presented, a sequence of 3 fors and the code execution has reached the third level (the innermost). After this goes through all its iterations you return to the second level for where you go to the next iteration in which you jump again in third level for. Similarly, when the second level finishes all its iteration you jump back to the first level for which continues with the next iteration in which you jump in the second level and from there in the third.
So, in a given level you try go to the deeper one (if there is one) and if there are no more iterations you go back a level (back track).
Using the backtracking you represent the nested for by an array where each element is an index variable: array[0] is the index for for level 0, and so on.
Here is a sample implementation for your problem:
#define NUMBER_OF_OBJECTS 10
#define FORLOOP_DEPTH 4 // This is equivalent with the number of
// of nested fors and in the problem is
// the number of requested objects
#define FORLOOP_ARRAY_INIT -1 // This is a init value for each "forloop" variable
#define true 1
#define false 0
typedef int bool;
int main(void)
{
int object_prices[NUMBER_OF_OBJECTS];
int forLoopsArray[FORLOOP_DEPTH];
bool isLoopVariableValueUsed[NUMBER_OF_OBJECTS];
int forLoopLevel = 0;
for (int i = 0; i < FORLOOP_DEPTH; i++)
{
forLoopsArray[i] = FORLOOP_ARRAY_INIT;
}
for (int i = 0; i < NUMBER_OF_OBJECTS; i++)
{
isLoopVariableValueUsed[i] = false;
}
forLoopLevel = 0; // Start from level zero
while (forLoopLevel >= 0)
{
bool isOkVal = false;
if (forLoopsArray[forLoopLevel] != FORLOOP_ARRAY_INIT)
{
// We'll mark the loopvariable value from the last iterration unused
// since we'll use a new one (in this iterration)
isLoopVariableValueUsed[forLoopsArray[forLoopLevel]] = false;
}
/* All iterations (in all levels) start basically from zero
* Because of that here I check that the loop variable for this level
* is different than the previous ones or try the next value otherwise
*/
while ( isOkVal == false
&& forLoopsArray[forLoopLevel] < (NUMBER_OF_OBJECTS - 1))
{
forLoopsArray[forLoopLevel]++; // Try a new value
if (loopVariableValueUsed[forLoopsArray[forLoopLevel]] == false)
{
objectUsed[forLoopsArray[forLoopLevel]] = true;
isOkVal = true;
}
}
if (isOkVal == true) // Have we found in this level an different item?
{
if (forLoopLevel == FORLOOP_DEPTH - 1) // Is it the innermost?
{
/* Here is the innermost level where you can test
* if the sum of all selected items is smaller than
* the target
*/
}
else // Nope, go a level deeper
{
forLoopLevel++;
}
}
else // We've run out of values in this level, go back
{
forLoopsArray[forLoopLevel] = FORLOOP_ARRAY_INIT;
forLoopLevel--;
}
}
}

How to draw a polygon from a set of unordered points

Currently, I am using a convex hull algorithm to get the outer most points from a set of points randomly placed. What I aim to do is draw a polygon from the set of points returned by the convex hull however, when I try to draw the polygon it looks quite strange.
My question, how do I order the points so the polygon draws correctly?
Thanks.
EDIT:
Also, I have tried sorting using orderby(...).ThenBy(...) and I cant seem to get it working.
Have you tried the gift wrapping algorithm ( http://en.wikipedia.org/wiki/Gift_wrapping_algorithm)? This should return points in the correct order.
I had an issue where a random set of points were generated from which a wrapped elevation vector needed a base contour. Having read the link supplied by #user1149913 and found a sample of gift-wrapping a hull, the following is a sample of my implementation:
private static PointCollection CalculateContour (List<Point> points) {
// locate lower-leftmost point
int hull = 0;
int i;
for (i = 1 ; i < points.Count ; i++) {
if (ComparePoint(points[i], points[hull])) {
hull = i;
}
}
// wrap contour
var outIndices = new int[points.Count];
int endPt;
i = 0;
do {
outIndices[i++] = hull;
endPt = 0;
for (int j = 1 ; j < points.Count ; j++)
if (hull == endPt || IsLeft(points[hull], points[endPt], points[j]))
endPt = j;
hull = endPt;
} while (endPt != outIndices[0]);
// build countour points
var contourPoints = new PointCollection(points.Capacity);
int results = i;
for (i = 0 ; i < results ; i++)
contourPoints.Add(points[outIndices[i]]);
return contourPoints;
}
This is not a full solution but a guide in the right direction. I faced a very similar problem just recently and I found a reddit post with an answer (https://www.reddit.com/r/DnDBehindTheScreen/comments/8efeta/a_random_star_chart_generator/dxvlsyt/) suggesting to use Delaunay triangulation which basically returns a solution with all possible triangles made within the data points you have. Once you have all possible triangles, which by definition you know won't result on any overlapped lines, you can chose which lines you use which result on all nodes being connected.
I was coding my solution on python and fortunately there's lots of scientific libraries on python. I was working on a random sky chart generator which would draw constellations out of those stars. In order to get all possible triangles (and draw them, just for fun), before going into the algorithm to draw the actual constellations, all I had to do was this:
# 2D array of the coordinates of every star generated randomly before
points = list(points_dict.keys())
from scipy.spatial import Delaunay
tri = Delaunay(points)
# Draw the debug constellation with the full array of lines
debug_constellation = Constellation(quadrants = quadrants, name_display_style = config.constellation_name_display_style)
for star in available_stars:
debug_constellation.add_star(star)
for triangle in tri.simplices:
star_ids = []
for index in triangle:
star_ids.append(points_dict[points[index]].id)
debug_constellation.draw_segment(star_ids, is_closed = True)
# Code to generate the image follows below
You can see the full implementation here: fake_sky_chart_generator/fake_libs/constellation_algorithms/delaunay.py
This is the result:

Arrays in Processing

I'm quite new to programming and have recently started in Processing.
In my code, the collide function sets the touch boolean to be true but by arraying it, it only tests true for the final array and not the ones before it. Where am I going wrong here? I hope my question is clear enough.
edit:
Sorry, let me try again.
I guess my problem is finding out how to array the collide function properly. I cant seem to add a [i] for the collide in the array.
At the moment, the code works but it only tests true for the last array and not for the ones before it.
The array code:
for(int i = 0 ; i < lineDiv; i++){
collide(xPts[i], yPts[i], vecPoints.xPos, vecPoints.yPos, myDeflector.Thk, vecPoints.d);
The collide function:
void collide(float pt1x, float pt1y, float pt2x, float pt2y, int size1, int size2){
if (pt1x + size1/2 >= pt2x - size2/2 &&
pt1x - size1/2 <= pt2x + size2/2 &&
pt1y + size1/2 >= pt2y - size2/2 &&
pt1y - size1/2 <= pt2y + size2/2) {
touch = true;
}
else{
touch=false;
}
Your "touch" variable is global. Every time you call the collide() function, it overwrites whatever it was set to before. Perhaps you just want to test if touch is true after calling collide(), then exit the for loop?
Alternatively, you may want to make collide() return the touch boolean, avoiding the global.
It looks like what you want to do is to run through a loop, run the function on that element of the array and return a value if any of them are true. This is my best guess, you might want to edit your question to clarify what you are looking to do. So assuming this:
1) change you method to a function
boolean collide(float pt1x, float pt1y, float pt2x, float pt2y, int size1, int size2){
if (pt1x + size1/2 >= pt2x - size2/2 &&
pt1x - size1/2 <= pt2x + size2/2 &&
pt1y + size1/2 >= pt2y - size2/2 &&
pt1y - size1/2 <= pt2y + size2/2) {
return true;
}
else{
return false;
}
2) change your loop and how you are calling it
touch = false; // if you don't set this to false before the loop, it will be the last value taken
for(int i = 0 ; i < lineDiv; i++){
if (collide(xPts[i], yPts[i], vecPoints.xPos, vecPoints.yPos, myDeflector.Thk, vecPoints.d)) touch = true;
Before the action would be that touch might cycle between true and false as you iterate through the array and in processing (because you would likely draw out the data) it is unlikely that you would want this behavior because you wouldn't be able to do anything with it unless you packed that data in another structure like an array.
So now, the "touch" is set to false and will change to true if any function calls return a true. If all are false, it will stay false.
note: you might consider using either xPts.length() or yPts.length() vs lineDiv. This would reduce the possibility of a array out of bounds exception assuming xPts and yPts have the same # of elements.

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