Sprite Kit: Rope with SKPhysicsJointLimit breaks under excessive force? - ios

The following code works great. It creates a dangling rope made of square links, and then applies a force to the bottom link to swing it around. It is executed in the SKScene object when the SKScene is created.
However, if you change the force on the last line from 2000 to 4000, the physics go haywire, and the links sometimes break. Sometimes the links seem to be vibrating or they’ll just submit entirely to gravity as if there is no joint. Additionally, if you have other physics bodies, they no longer collide with the haywire links, even if they did before the force was applied.
Although 4000 seems excessive, I’ve encountered this issue with much less force on lighter objects, or smaller forces on ropes with less of a gap between links.
Am I doing something wrong? Is there a bug in Sprite Kit or some other explanation? I couldn’t find any answers online.
It also doesn't matter if the force is applied during SKScene creation or delayed until later.
self.scaleMode = SKSceneScaleModeAspectFit;
self.anchorPoint = CGPointMake(0.5, 0.5);
CGFloat length = 20;
CGFloat gapMult = 1.8;
int numBoxes = 10;
SKSpriteNode *prevBox = nil;
for (int i = 0; i < numBoxes; i++) {
SKSpriteNode *box = [SKSpriteNode spriteNodeWithColor:[UIColor yellowColor] size:CGSizeMake(length, length)];
box.position = CGPointMake(0, -i * length * gapMult);
[self addChild:box];
box.physicsBody = [SKPhysicsBody bodyWithRectangleOfSize:CGSizeMake(length, length)];
if (i == 0) {
box.physicsBody.dynamic = NO;
} else {
CGPoint pt1 = CGPointMake(0, prevBox.position.y - length / 2);
CGPoint pt2 = CGPointMake(0, box.position.y + length / 2);
SKPhysicsJointLimit *joint = [SKPhysicsJointLimit jointWithBodyA:prevBox.physicsBody bodyB:box.physicsBody anchorA:pt1 anchorB:pt2];
[self.physicsWorld addJoint:joint];
}
prevBox = box;
}
[prevBox.physicsBody applyForce:CGVectorMake(2000, 0)];

Related

Sticking nodes to SkSpriteNode after enlargement

Problem
As of right now, I've just realised a pretty major design flaw in my application..
So, the problem is:
A rifle shot is fired, and lands based on no trajectory as of right now, I'm toying with the idea. However, the bullets land and their marks are left as nodes.
-(void)applyShot:(int) posX with:(int) posY {
SKSpriteNode *impact = [[SKSpriteNode alloc] initWithColor:[UIColor grayColor] size:CGSizeMake(2, 2)];
impact.zPosition = 1;
impact.userInteractionEnabled = NO;
impact.position = CGPointMake(posX , posY);
[backgroundImage addChild:impact];
}
And posX / posY are sent this way.
//Find difference between centre and background moved distance.
CGPoint positionNow = CGPointMake(backgroundImage.position.x, backgroundImage.position.y);
CGPoint positionPrev = CGPointMake(0.5, 0.5);
float xdiff = positionNow.x - positionPrev.x;
float ydiff = positionNow.y - positionPrev.y;
//Calculate ydrop
int newYDrop = yDrop * 10;
//
CGPoint newPositionOne = CGPointMake(0.5 - xdiff, 0.5 - ydiff);
newPositionOne = CGPointMake((newPositionOne.x + [self myRandom:15 withFieldLower:-15]), (newPositionOne.y - newYDrop));
dispatch_after(dispatch_time(DISPATCH_TIME_NOW, (int64_t)(secondsDelay * NSEC_PER_SEC)), dispatch_get_main_queue(), ^(void){
[self applyShot:newPositionOne.x with:newPositionOne.y];
});
Which seems to work fine, until I started toying with zoom.
Now, this application basically is a 1080p image for the reticle, and the background enlarges to give the (zoom) effect, then the background is touch-dragged/inverted to give the reticle moving effect.
Then I managed to get it to fire exactly where the crosshair was, which was good.. Then I started toying with zoom and noticed this.
So if it's not too easy to notice, the (bullet hits) are the grey marks, however, when you enlarge the backgroundImage they aren't tied to it. so they remain the same spread.
Solution
Now what I need is to either,
A: tie the nodes to the backgroundImage
B: enlarge the spread to the same factor as the enlargement.
But I'm pretty confused at how to achieve this.
Additional problem
When calibrating the drop, the drop will remain a burden no matter of the zoom as of right now. so if it's a 1 mil-dot drop on 6x zoom, it's also a 1 mil-dot drop at 10x zoom or 1x zoom ( I keep saying zoom when I mean enlargement )
How can I achieve a calibration for drop intensity no matter what enlargement the background image is at?
Thanks for reading and confusing yourself with my dire problems, it's appreciated!
What I've Tried
saving the children to a mutable array, then recreating them after a zoom change;
//recreate children
[backgroundImage removeAllChildren];
for (int i=0; i < [shotsHitX count]; i++) {
double posX = ([shotsHitX[i] doubleValue] / 5) * rifleZoom;
double posY = ([shotsHitY[i] doubleValue] / 5) * rifleZoom;
SKSpriteNode *impact = [[SKSpriteNode alloc] initWithColor:[UIColor grayColor] size:CGSizeMake(2, 2)];
impact.zPosition = 1;
impact.userInteractionEnabled = NO;
impact.position = CGPointMake(posX , posY);
[shotsHitX addObject:[NSNumber numberWithDouble:posX]];
[shotsHitY addObject:[NSNumber numberWithDouble:posY]];
[backgroundImage addChild:impact];
}
//end recreate children
Crash with memory error.
not so good at this!
[backgroundImage removeAllChildren];
for (int i=0; i < [shotsHitX count]; i++) {
double posX = ([shotsHitX[i] doubleValue] / 5) * rifleZoom;
double posY = ([shotsHitY[i] doubleValue] / 5) * rifleZoom;
SKSpriteNode *impact = [[SKSpriteNode alloc] initWithColor:[UIColor grayColor] size:CGSizeMake(2, 2)];
impact.zPosition = 1;
impact.userInteractionEnabled = NO;
impact.position = CGPointMake(posX , posY);
[backgroundImage addChild:impact];
}
//end recreate children
Works, however, now It doesn't just seem quite right..
I think the problem is when the initial zoom goes in it works, then when it reverts it's mixing zoom shots in the array with old shots.. Here we go again, MORE ARRAYS.
//recreate children
[backgroundImage removeAllChildren];
for (int i=0; i < [shotsHitRem count]; i+= 2) {
double posX = ([shotsHitRem[i] doubleValue] / 5) * rifleZoom;
double posY = ([shotsHitRem[i+1] doubleValue] / 5) * rifleZoom;
SKSpriteNode *impact = [[SKSpriteNode alloc] initWithColor:[UIColor grayColor] size:CGSizeMake(2, 2)];
impact.zPosition = 1;
impact.userInteractionEnabled = NO;
impact.position = CGPointMake(posX , posY);
[backgroundImage addChild:impact];
//add olds m4
if ([shotsHitM4 count] > 0) {
posX = ([shotsHitM4[i] doubleValue] / 2) * rifleZoom;
posY = ([shotsHitM4[i+1] doubleValue] / 2) * rifleZoom;
impact.position = CGPointMake(posX, posY);
[backgroundImage addChild:impact];
}
}
//end recreate children
Now I crash attempting to add a sknode which already has a parent
Confusing as it should removeAllChildren before looping
Well after some major messing around
[backgroundImage setScale:rifleZoom];
Programming is my favourite, oh yeah.. Five hours, Oh yeah.. For one line, oh yeah!
I wasn't scaling before, I was creating a new cgsize. and that was my problem.
I now have the issue of scaling and trying to render a new centrepoint as it still remembers the centrepoint of scale = 1 and scale = 2, nightmare.

Fixed floor in Sprite Kit Xcode

I can't seem to get a unmovable fixed floor / wall in Sprite Kit.
I have a scene which has an SKNode as a "floor" and when the user presses the screen, a block drops from the touched position onto the "floor". That works well, but when the user adds another lets say 20 blocks or so, suddenly the floor rotates.
This is the code for my Floor:
SKSpriteNode *floorNode = [[SKSpriteNode alloc] initWithColor:[SKColor clearColor] size:CGSizeMake(self.size.width*2, 10)];
floorNode.position = CGPointMake(CGRectGetMidX(self.frame), -5);
floorNode.name = #"floor";
floorNode.zPosition = 1;
floorNode.physicsBody = [SKPhysicsBody bodyWithRectangleOfSize:floorNode.size];
floorNode.physicsBody.affectedByGravity = NO;
floorNode.physicsBody.dynamic = NO;
floorNode.physicsBody.usesPreciseCollisionDetection = YES;
return floorNode;
Sorry i'm quite new to Sprite Kit. Does anyone know what's wrong with my code?
EDIT: I've added some images to make the problem a bit more clear. Since it happens in this screen also. Those black spheres you see are flying from left to right like a canonball. I increased the amount of spheres to show the problem occurring. This is the code:
- (SKNode *)newEditButton {
SKLabelNode *editButtonNode = [SKLabelNode labelNodeWithFontNamed:#"chalkduster"];
editButtonNode.text = #"EDIT CASTLE";
editButtonNode.fontSize = 19;
editButtonNode.fontColor = [SKColor darkGrayColor];
editButtonNode.position = CGPointMake(CGRectGetMidX(self.frame) + 110, CGRectGetMidY(self.frame) + 30);
editButtonNode.name = #"edit_button";
editButtonNode.zPosition = 2;
editButtonNode.physicsBody = [SKPhysicsBody bodyWithRectangleOfSize:CGSizeMake(140, 40)];
editButtonNode.physicsBody.usesPreciseCollisionDetection = YES;
editButtonNode.physicsBody.dynamic = NO;
editButtonNode.physicsBody.affectedByGravity = NO;
SKAction *hover = [SKAction sequence:#[[SKAction moveByX:0 y:6.0 duration:0.9],
[SKAction moveByX:0 y:-6.0 duration:0.9]]];
SKAction *hoverForever = [SKAction repeatActionForever:hover];
[editButtonNode runAction:hoverForever];
return editButtonNode;
}
- (SKNode *)newPlayButton {
SKLabelNode *playButtonNode = [SKLabelNode labelNodeWithFontNamed:#"chalkduster"];
playButtonNode.text = #"SLAUGHTER";
playButtonNode.fontSize = 19;
playButtonNode.fontColor = [SKColor darkGrayColor];
playButtonNode.position = CGPointMake(CGRectGetMidX(self.frame) - 110, CGRectGetMidY(self.frame) + 30);
playButtonNode.name = #"play_button";
playButtonNode.zPosition = 2;
playButtonNode.physicsBody = [SKPhysicsBody bodyWithRectangleOfSize:CGSizeMake(140, 40)];
playButtonNode.physicsBody.usesPreciseCollisionDetection = YES;
playButtonNode.physicsBody.dynamic = NO;
playButtonNode.physicsBody.affectedByGravity = NO;
SKAction *hover = [SKAction sequence:#[[SKAction moveByX:0 y:6.0 duration:0.9],
[SKAction moveByX:0 y:-6.0 duration:0.9]]];
SKAction *hoverForever = [SKAction repeatActionForever:hover];
[playButtonNode runAction:hoverForever];
return playButtonNode;
}
After a while 5-10 seconds, the "buttons" called "slaughter" and "edit castle" start to rotate everytime a sphere collides with it. But it doesn't seem like it has to do something with physics, because, if it rotates to the left, it's rotation direction will always be left. And if it starts rotating right, it's rotation direction will always be right.
It looks funny though! But not what i want ;-)
You don't know it, but you're telling SpriteKit to apply collisions from the cannonballs to the labels, and from the blocks to the floor!
That's because you're leaving SKPhysicsBody.collisionBitMask to its default value, which is to observe collisions for everything.
From the documentation:
Discussion
When two physics bodies contact each other, a collision may occur. This body’s collision mask is compared to the other body’s category mask by performing a logical AND operation. If the result is a nonzero value, this body is affected by the collision. Each body independently chooses whether it wants to be affected by the other body. For example, you might use this to avoid collision calculations that would make negligible changes to a body’s velocity.
The default value is 0xFFFFFFFF (all bits set).
So, do:
floorNode.physicsBody.collisionBitMask = 0

iOS - SpriteKit : ApplyImpulse not working on SKSpriteNode

I'm kind of new with SpriteKit and I'm having some troubles with the physics, I've tried many things to make a SKSpriteNode move with a force or an impulse but it never moves, only gravity affects it when i set it.
-(id)initWithSize:(CGSize)size {
if (self = [super initWithSize:size]) {
self.anchorPoint = CGPointMake(0.5, 0.5);
myWorld = [SKNode node];
[self addChild:myWorld];
SKSpriteNode* map = [SKSpriteNode spriteNodeWithImageNamed:#"grass"];
[myWorld addChild:map];
self.physicsBody = [SKPhysicsBody bodyWithEdgeLoopFromRect:map.frame];
self.physicsBody.friction = 0.0f;
self.physicsBody.categoryBitMask = 2;
self.physicsWorld.gravity = CGVectorMake(0.0, 0.0);
self.physicsWorld.contactDelegate = self;
pointOfView = [SKSpriteNode spriteNodeWithColor:[UIColor colorWithWhite:1 alpha:0.2] size:CGSizeMake(300, 548)];
[myWorld addChild:pointOfView];
pointOfView.physicsBody = [SKPhysicsBody bodyWithRectangleOfSize:pointOfView.frame.size];
pointOfView.physicsBody.friction = 0.0f;
pointOfView.physicsBody.restitution = 1.0f;
pointOfView.physicsBody.linearDamping = 0.0f;
pointOfView.physicsBody.allowsRotation = NO;
pointOfView.physicsBody.collisionBitMask = 2;
pointOfView.physicsBody.categoryBitMask = 3;
[pointOfView.physicsBody applyImpulse:CGVectorMake(10.0f, -10.0f)];
}
return self;
}
Here is most of my code in my main scene, there's nothing else except some empty methods like update or touchesBegan.. Am I missing something ? I've tried so many things, i'm starting to lose it haha
Thanks very much for any help !
It's a bit late, but the answer is here: Not able to apply impulse to SKSpriteNode physics body
The problem is that you've created a physics body with bodyWithEdgeLoopFromRect; this creates a static physics body which won't respond to applyImpulse. You need to add the physics body using bodyWithRectangleOfSize: instead.
pointOfView.physicsBody.dynamic = YES;
The dynamic property decides if a sprite should be affected by physics forces.
you have written wrong code your pointOfView not affected by gravity you are just applying a small impusle on it.
change this line self.physicsWorld.gravity = CGVectorMake(0.0, 0.0) to self.physicsWorld.gravity = CGVectorMake(0.0, -9.8); if u looking for negative gravity towards up direction and CGVectorMake(0.0, 9.8) if you looking for positive gravity towards downwards. and try to apply impulse after a interval [pointOfView.physicsBody applyImpulse:CGVectorMake(10.0f, -10.0f)];

How can I keep my sprites velocity constant?

I'm making a simple space shooter in Sprite Kit. I have asteroid rock sprites that are randomly added to my scene. I give them a random velocity within a certain range. However, once added to the scene their velocity decreases every second and eventually they stop. as they get closer to the bottom of the screen their velocity decreases at a slower rate. I have gravity of my physics world set to (0,0).
below is the method that adds the rocks to the scene
- (void)addRock {
SPRockNode *rock = [SPRockNode rock];
float dy = [SPUtil randomWithMin:SPRockMinSpeed max:SPRockMaxSpeed];
rock.physicsBody.velocity = CGVectorMake(0, -dy);
float y = self.frame.size.height + rock.size.height;
float x = [SPUtil randomWithMin:10 + rock.size.width max:self.frame.size.width - 10 - rock.size.width];
rock.position = CGPointMake(x, y);
[self addChild:rock];
}
I set up the physics world in my scenes initWIthSize method
self.physicsWorld.contactDelegate = self;
self.physicsWorld.gravity = CGVectorMake(0, 0);
below is the code for my rock node class
+ (instancetype)rock {
SPRockNode *rock = [self spriteNodeWithImageNamed:#"rock"];
rock.name = #"Rock";
float scale = [SPUtil randomWithMin:50 max:100] / 100.0f;
rock.xScale = scale;
rock.yScale = scale;
NSInteger randomInt = [SPUtil randomWithMin:1 max:3];
if (randomInt == 1) {
SKAction *oneRevolution = [SKAction rotateByAngle:-M_PI*2 duration: 1.0];
SKAction *repeat = [SKAction repeatActionForever:oneRevolution];
[rock runAction:repeat];
} else {
SKAction *oneRevolution = [SKAction rotateByAngle:M_PI*2 duration: 1.0];
SKAction *repeat = [SKAction repeatActionForever:oneRevolution];
[rock runAction:repeat];
}
[rock setupPhysicsBody];
return rock;
}
- (void)setupPhysicsBody {
self.physicsBody = [SKPhysicsBody bodyWithRectangleOfSize:self.frame.size];
self.physicsBody.affectedByGravity = NO;
self.physicsBody.categoryBitMask = SPCollisionCategoryRock;
self.physicsBody.collisionBitMask = 0;
self.physicsBody.contactTestBitMask = SPCollisionCategoryProjectile | SPCollisionCategoryShip;
}
any ideas on what causing them to slow down? I dont modify their velocity anywhere else but the addRock method. is there air resistance or something like that on by default? I just dont understand why their velocity is decreasing.
It sounds like you are having an issue with linear damping.
From SKPhysicsBody reference :
This property is used to simulate fluid or air friction forces on the body. The property must be a value between 0.0 and 1.0. The default value is 0.1. If the value is 0.0, no linear damping is applied to the object.
Try adding this :
rock.physicsBody.linearDamping = 0.0f;
It's worthwhile to give the SKPhysicsBody class reference a reading at least once. It only takes a short while, but can save you a ton of time if you have become acquainted with it's properties and methods.

dynamic cone shape changes depending on obstacles - reference to Third Eye Crime app

I've seen the Trailer of "Third Eye Crime".
How can you realise the blue field of view cone so that it's shape changes depending on obstacles?
My attempt was to cast rays till an obstacle occurs and then I take the end points of the rays to draw the cone shape.
The problem with my method is that the precision of the cone depends on the number of rays. Besides the more rays are casted the worse the performance.
Here you can see the rays:
Here you can see the cone shape drawn with the end points of the rays:
Are there better solutions?
Your question has been bugging me all day but I can't find a fully working answer. My work notes are too much for me to write it as a comment so I am adding it as an answer.
My first issue was to test for a contact between a field of view line and any obstruction object. Unfortunately SpriteKit only has the contactBitMask which can do this job AND provide contact coordinates.
I looked at SKNode's intersectsNode: but its return value is only a BOOL and we need coordinates.
I also looked at Apple's Sprite Kit Programming Guide's section Searching for Physics Bodies. This deals with line of sight, obstacles, etc... The command used here is bodyAlongRayStart:end:. The return is the first physics body it intersects with but without providing the coordinates for the actual contact point.
The code I ended up with first draws the complete line of sight cone. Next any lines found contacting an object got the contact point using contact.contactPoint and then deleted the offending line. So far so good. But I ran into trouble trying to draw the deleted line to the new end point (contact point). For some inexplicable reason only some of the deleted lines are being redrawn and not all.
Keep in mind this is rough code so slap it, pull it and throw it against the wall a couple of times. You don't really need the array for example. I hope this will steer you in the right direction or you can spot something I am too blind to see.
Side note: I ran this in simulator iPhone (4 inch) landscape.
#import "MyScene.h"
typedef NS_OPTIONS(uint32_t, CNPhysicsCategory)
{
Category1 = 1 << 0,
Category2 = 1 << 1,
Category3 = 1 << 2,
};
#interface MyScene()<SKPhysicsContactDelegate>
#end
#implementation MyScene
{
SKSpriteNode *player;
SKSpriteNode *obstacle1;
SKSpriteNode *obstacle2;
SKSpriteNode *obstacle3;
SKSpriteNode *obstacle4;
NSMutableArray *beamArray;
int beamCounter;
}
-(id)initWithSize:(CGSize)size
{
if (self = [super initWithSize:size])
{
self.physicsWorld.contactDelegate = self;
beamArray = [[NSMutableArray alloc] init];
beamCounter = 0;
player = [SKSpriteNode spriteNodeWithColor:[SKColor redColor] size:CGSizeMake(20, 20)];
player.position = CGPointMake(100, 150);
[self addChild:player];
obstacle1 = [SKSpriteNode spriteNodeWithColor:[SKColor blueColor] size:CGSizeMake(200, 20)];
obstacle1.name = #"obstacle1";
obstacle1.position = CGPointMake(250, 100);
obstacle1.physicsBody = [SKPhysicsBody bodyWithRectangleOfSize:obstacle1.size];
obstacle1.physicsBody.affectedByGravity = NO;
obstacle1.physicsBody.categoryBitMask = Category2;
obstacle1.physicsBody.collisionBitMask = 0x00000000;
[self addChild:obstacle1];
obstacle2 = [SKSpriteNode spriteNodeWithColor:[SKColor blueColor] size:CGSizeMake(40, 40)];
obstacle2.name = #"obstacle2";
obstacle2.position = CGPointMake(400, 200);
obstacle2.physicsBody = [SKPhysicsBody bodyWithRectangleOfSize:obstacle2.size];
obstacle2.physicsBody.affectedByGravity = NO;
obstacle2.physicsBody.categoryBitMask = Category2;
obstacle2.physicsBody.collisionBitMask = 0x00000000;
[self addChild:obstacle2];
obstacle3 = [SKSpriteNode spriteNodeWithColor:[SKColor blueColor] size:CGSizeMake(50, 20)];
obstacle3.name = #"obstacle3";
obstacle3.position = CGPointMake(530, 130);
obstacle3.physicsBody = [SKPhysicsBody bodyWithRectangleOfSize:obstacle3.size];
obstacle3.physicsBody.affectedByGravity = NO;
obstacle3.physicsBody.categoryBitMask = Category2;
obstacle3.physicsBody.collisionBitMask = 0x00000000;
[self addChild:obstacle3];
for (int y = 0; y <= 320; y++)
{
SKShapeNode *beam1 = [SKShapeNode node];
beam1.name = [NSString stringWithFormat:#"%i",beamCounter++];
CGMutablePathRef pathToDraw = CGPathCreateMutable();
CGPathMoveToPoint(pathToDraw, NULL, player.position.x, player.position.y);
CGPathAddLineToPoint(pathToDraw, NULL, 600, y);
beam1.path = pathToDraw;
[beam1 setStrokeColor:[UIColor yellowColor]];
[beam1 setLineWidth:2.0];
beam1.physicsBody = [SKPhysicsBody bodyWithEdgeFromPoint:CGPointMake(player.position.x, player.position.y) toPoint:CGPointMake(600, y)];
beam1.physicsBody.affectedByGravity = NO;
beam1.physicsBody.categoryBitMask = Category1;
beam1.physicsBody.contactTestBitMask = Category2;
[self addChild:beam1];
[beamArray addObject:beam1];
}
}
return self;
}
-(void)touchesBegan:(NSSet *)touches withEvent:(UIEvent *)event
{
//
}
-(void)update:(CFTimeInterval)currentTime
{
//
}
- (void)didBeginContact:(SKPhysicsContact *)contact
{
NSLog(#"bodyA:%# bodyB:%#",contact.bodyA.node.name, contact.bodyB.node.name);
uint32_t collision = (contact.bodyA.categoryBitMask | contact.bodyB.categoryBitMask);
if (collision == (Category1 | Category2))
{
CGPoint newEndPoint = contact.contactPoint;
[beamArray removeObject:contact.bodyA.node.name];
[contact.bodyA.node removeFromParent];
SKShapeNode *beam1 = [SKShapeNode node];
beam1.name = [NSString stringWithFormat:#"%i",beamCounter++];
CGMutablePathRef pathToDraw = CGPathCreateMutable();
CGPathMoveToPoint(pathToDraw, NULL, player.position.x, player.position.y);
CGPathAddLineToPoint(pathToDraw, NULL, newEndPoint.x, newEndPoint.y);
beam1.path = pathToDraw;
[beam1 setStrokeColor:[UIColor greenColor]];
[beam1 setLineWidth:2.0];
[self addChild:beam1];
}
}
#end
Removing the touching lines:
Removing the touching lines and replacing the removed lines:
How I would do it is send out a ray at the edges of view and make note of the points that they hit. Then find points that are important(corners of objects for example), form rays with those points and use those rays to find collisions past those points and finally fill triangles with the points and the "source" of the light.
I might get a chance to make pictures to help demonstrate my algorithm later but this is what I have now.
I think the efficient way to do this is to use Bresenham's Algorithm. There are lots of references and example code in the Wikipedia references section.
http://en.wikipedia.org/wiki/Bresenham%27s_line_algorithm
Here I've found several answers:
https://code.google.com/p/straightedge/
http://www.redblobgames.com/articles/visibility/

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