# 2d rotating polygon collision example using planes.

I wrote out this little example after speaking in a post about how you can use the dot and cross product to find collisions against points of other objects. The example shows how directions and normals equate to planes or surfaces using the dot product shown in the image by the red and green lines.

This example requires no content to be loaded just copy paste of the posted class files as per instruction above the given code.

One use for this is for creating collision polygons for images then use it instead of a costly per pixel check when working with them.

While this is a 2d example this can also be used for 3d objects by building bounding polyhedrons around objects or just selecting and using some of the existing models current triangles as planes to effect a check.

This can be combined with a broad phase model sized bounding rectangle as a secondary level of check that can be as basic or accurate as the creator desires and other techniques can be combined to refine or speed it up further.

This example uses a Rectangle which is a type of polygon.
Itâ€™s not made to be performant or refined.
It is only to demonstrate the basic principals.

To use it create a new project replace the game1 class code within the game1.cs file with the following code and run the project.

``````// it uses the following names spaces as well.
//using System;
//using Microsoft.Xna.Framework;
//using Microsoft.Xna.Framework.Graphics;
//using Microsoft.Xna.Framework.Input;

public class Game1 : Game
{
public static GraphicsDeviceManager graphics;
public static SpriteBatch spriteBatch;
public static SpriteFont font;

Rectangle posRectangle0 = new Rectangle(100, 100, 100, 100);
Rectangle posRectangle1 = new Rectangle(220, 100, 100, 100);

Rectangle posRectangle3 = new Rectangle(100, 250, 100, 100);
Rectangle posRectangle4 = new Rectangle(220, 250, 100, 100);

float rotationcc = 0.4f;
float rotationccw = -.4f;

public Game1()
{
graphics = new GraphicsDeviceManager(this);
Content.RootDirectory = "Content";
}
protected override void Initialize()
{
// TODO: Add your initialization logic here

base.Initialize();
}
protected override void LoadContent()
{
// Create a new SpriteBatch, which can be used to draw textures.
spriteBatch = new SpriteBatch(GraphicsDevice);

// TODO: use this.Content to load your game content here
ExampleHelperClass.SetUp(graphics, ref spriteBatch);

}
protected override void UnloadContent()
{
// TODO: Unload any non ContentManager content here
}
protected override void Update(GameTime gameTime)
{
if (GamePad.GetState(PlayerIndex.One).Buttons.Back == ButtonState.Pressed || Keyboard.GetState().IsKeyDown(Keys.Escape))
Exit();

// TODO: Add your update logic here
rotationcc += .003f;
rotationcc = ExampleHelperClass.AlignRotation(rotationcc);
rotationccw -= .003f;
rotationccw = ExampleHelperClass.AlignRotation(rotationccw);

base.Update(gameTime);
}
protected override void Draw(GameTime gameTime)
{
GraphicsDevice.Clear(Color.White);

spriteBatch.Begin();

Color color0 = Color.Beige;
if (ExampleHelperClass.IsRectangleWithinCollisionRectangle(posRectangle0, rotationcc, false, posRectangle1, rotationccw, false))
{
color0 = Color.Red;
}
else
{
color0 = Color.Green;
}
//spriteBatch.Draw(MiscDraw.dotTexture, posRectangle0, MiscDraw.dotRectangle, Color.Black, rotationcc, Vector2.Zero, SpriteEffects.None, 0);
//spriteBatch.Draw(MiscDraw.dotTexture, posRectangle1, MiscDraw.dotRectangle, Color.Black, rotationccw, Vector2.Zero, SpriteEffects.None, 0);

ExampleHelperClass.DrawBasicSquare(posRectangle0, 1, color0, false, false, rotationcc);
ExampleHelperClass.DrawBasicSquare(posRectangle1, 1, color0, false, false, rotationccw);

Color color1 = Color.Black;
if (ExampleHelperClass.IsRectangleWithinCollisionRectangle(posRectangle3, rotationcc, true, posRectangle4, rotationccw, true))
{
color1 = Color.Red;
}
else
{
color1 = Color.Green;
}
//MiscDraw.DrawCenteredRotatedRectangle(MiscDraw.dotTexture, posRectangle3, MiscDraw.dotRectangle, rotationcc, Color.AliceBlue);
//MiscDraw.DrawCenteredRotatedRectangle(MiscDraw.dotTexture, posRectangle4, MiscDraw.dotRectangle, rotationccw, Color.AliceBlue);

ExampleHelperClass.DrawBasicSquare(posRectangle3, 1, color1, false, true, rotationcc);
ExampleHelperClass.DrawBasicSquare(posRectangle4, 1, Color.Blue, false, true, rotationccw);

spriteBatch.End();

base.Draw(gameTime);
}
}

public static class ExampleHelperClass
{
public const float PI = (float)(Math.PI);
public const float PI2 = (float)(Math.PI * 2);
public const float PIHALF = (float)(Math.PI * .5f);
public const float TORADIANS = PI2 / 360.0f;
public const float TODEGREES = 360.0f / PI2;

static SpriteBatch spriteBatch;
public static Texture2D dotTexture;
public static Rectangle dotRectangle = new Rectangle(0, 0, 1, 1);

public static void SetUp(GraphicsDeviceManager gdm, ref SpriteBatch sb)
{
spriteBatch = sb;
if (dotTexture == null)
{
dotTexture = TextureDotCreate(gdm.GraphicsDevice);
}
}

public static Texture2D TextureDotCreate(GraphicsDevice device)
{
Color[] data = new Color[1];
data[0] = new Color(255, 255, 255, 255);

return TextureFromColorArray(device, data, 1, 1);
}
public static Texture2D TextureFromColorArray(GraphicsDevice device, Color[] data, int width, int height)
{
if (width > 2047 || height > 2047)
{
Console.WriteLine(" TextureFromColorArray(...) -> Big ass array to texture !");
}
Texture2D tex = new Texture2D(device, width, height);
tex.SetData<Color>(data);
return tex;
}

public static void DrawBasicPoint(Vector2 p, Color c)
{
Rectangle screendrawrect = new Rectangle((int)p.X, (int)p.Y, 2, 2);
spriteBatch.Draw(dotTexture, screendrawrect, new Rectangle(0, 0, 1, 1), c, 0.0f, Vector2.One, SpriteEffects.None, 0);
}
public static void DrawLine(Vector2 postion, int length, int linethickness, float rot, Color c)
{
Rectangle screendrawrect = new Rectangle((int)postion.X, (int)postion.Y, linethickness, length);
spriteBatch.Draw(dotTexture, screendrawrect, new Rectangle(0, 0, 1, 1), c, rot, Vector2.Zero, SpriteEffects.None, 0);
}
public static void DrawBasicLine(Vector2 s, Vector2 e, int thickness, Color linecolor, float rot)
{
float distance = Vector2.Distance(s, e);
float direction = (float)Atan2Xna(e.X - s.X, e.Y - s.Y);
//direction = DirectionToRadians(e.X - s.X, e.Y - s.Y);
direction += rot;
Rectangle screendrawrect = new Rectangle((int)s.X, (int)s.Y, thickness, (int)distance);
spriteBatch.Draw(dotTexture, screendrawrect, new Rectangle(0, 0, 1, 1), linecolor, direction, Vector2.Zero, SpriteEffects.None, 0);
}
public static void DrawBasicLine(Vector2 s, Vector2 e, int thickness, Color linecolor)
{
float distance = Vector2.Distance(e, s); ;
float direction = (float)Atan2Xna(e.X - s.X, e.Y - s.Y);
Rectangle screendrawrect = new Rectangle((int)s.X, (int)s.Y, thickness, (int)distance);
spriteBatch.Draw(dotTexture, screendrawrect, new Rectangle(0, 0, 1, 1), linecolor, direction, Vector2.Zero, SpriteEffects.None, 0);
}

public static void DrawBasicSquare(Rectangle r, int thickness, Color col, bool draw_filled, bool drawCentered, float rotation)
{
if (drawCentered)
DrawBasicSquare(r, thickness, col, draw_filled, rotation, new Vector2(r.X + r.Width * .5f, r.Y + r.Height * .5f));
else
DrawBasicSquare(r, thickness, col, draw_filled, rotation, new Vector2(r.X, r.Y));
}
public static void DrawBasicSquare(Rectangle r, int thickness, Color col, bool draw_filled, float rotation, Vector2 rotOrigin)
{
if (draw_filled == false)
{
float q = rotation;
Vector2 A = new Vector2(r.Left, r.Top);
Vector2 B = new Vector2(r.Right, r.Top);
Vector2 C = new Vector2(r.Right, r.Bottom);
Vector2 D = new Vector2(r.Left, r.Bottom);
Vector2 o = rotOrigin;
A = Rotate2dPointAboutOriginOnZaxis(A, o, q);
B = Rotate2dPointAboutOriginOnZaxis(B, o, q);
C = Rotate2dPointAboutOriginOnZaxis(C, o, q);
D = Rotate2dPointAboutOriginOnZaxis(D, o, q);
ExampleHelperClass.DrawLine(A, r.Width, thickness, q, col);
ExampleHelperClass.DrawLine(B, r.Height, thickness, q + PIHALF, col);
ExampleHelperClass.DrawLine(C, r.Width, thickness, q + (PIHALF * 2), col);
ExampleHelperClass.DrawLine(D, r.Height, thickness, q + (PIHALF * 3), col);
}
else
{
spriteBatch.Draw(dotTexture, r, new Rectangle(0, 0, 1, 1), col, rotation, rotOrigin, SpriteEffects.None, 0);
}
}

/* collision stuff */

// didnt test
public static bool IsUnrotatedRectanglesColliding(Rectangle r0, Rectangle r1)
{
Point cd = r1.Center - r0.Center;
if (cd.X < 0) { cd.X = -cd.X; }
if (cd.Y < 0) { cd.Y = -cd.Y; }
Point gwh = new Point( (int)((r0.Width + r1.Width) * .5f), (int)((r0.Height + r1.Height) * .5f));
if(cd.X<gwh.X && cd.Y<gwh.Y)
return true;
else
return false;
}

// rotated simple origins
public static bool IsRectangleWithinCollisionRectangle(Rectangle r0, float rotationR0, bool centerOriginR0, Rectangle r1, float rotationR1, bool centerOriginR1)
{
Vector2 org0 = new Vector2(r0.X, r0.Y);
if (centerOriginR0)
org0 = new Vector2(r0.X + r0.Width * .5f, r0.Y + r0.Height * .5f);

Vector2 org1 = new Vector2(r1.X, r1.Y);
if (centerOriginR1)
org1 = new Vector2(r1.X + r1.Width * .5f, r1.Y + r1.Height * .5f);

return IsRectangleWithinCollisionRectangle(r0, rotationR0, org0, r1, rotationR1, org1);
}

// rotated 0,0 is the coordinate system origin
public static bool IsRectangleWithinCollisionRectangle(Rectangle r0, float rotationR0, Vector2 rotOriginR0, Rectangle r1, float rotationR1, Vector2 rotOriginR1)
{
// This can be any shape its not limited to rectangles its basically a polygon boundry check.
// typically you use arrays however im going to use variables step by step.

// get rotated points of rectangle 1
Vector2 A0 = new Vector2(r0.Left, r0.Top);
Vector2 B0 = new Vector2(r0.Right, r0.Top);
Vector2 C0 = new Vector2(r0.Right, r0.Bottom);
Vector2 D0 = new Vector2(r0.Left, r0.Bottom);
// optimally you store the shapes points in clockwise (cw) or ccw order.
// we could also do this with just two rotations saving a lot of this extra work
A0 = Rotate2dPointAboutOriginOnZaxis(A0, rotOriginR0, rotationR0);
B0 = Rotate2dPointAboutOriginOnZaxis(B0, rotOriginR0, rotationR0);
C0 = Rotate2dPointAboutOriginOnZaxis(C0, rotOriginR0, rotationR0);
D0 = Rotate2dPointAboutOriginOnZaxis(D0, rotOriginR0, rotationR0);

// get rotated points of rectangle 2
Vector2 A1 = new Vector2(r1.Left, r1.Top);
Vector2 B1 = new Vector2(r1.Right, r1.Top);
Vector2 C1 = new Vector2(r1.Right, r1.Bottom);
Vector2 D1 = new Vector2(r1.Left, r1.Bottom);
A1 = Rotate2dPointAboutOriginOnZaxis(A1, rotOriginR1, rotationR1);
B1 = Rotate2dPointAboutOriginOnZaxis(B1, rotOriginR1, rotationR1);
C1 = Rotate2dPointAboutOriginOnZaxis(C1, rotOriginR1, rotationR1);
D1 = Rotate2dPointAboutOriginOnZaxis(D1, rotOriginR1, rotationR1);

// you can return true with just one match but this is left to demonstrate.
bool match = false;

// first rectangle
// well use this to give more visual info to the user
if(IsPointWithinRectangleDisplay(A0, B0, C0, D0, A1, false)) { match = true; }
// in 2d also with just rectangles we could do this with just 2 points a target and a normal
// per rectangle but since this is a demo
if (IsPointWithinRectangle(A0, B0, C0, D0, B1, false)) { match = true; }
if (IsPointWithinRectangle(A0, B0, C0, D0, C1, false)) { match = true; }
if (IsPointWithinRectangle(A0, B0, C0, D0, D1, false)) { match = true; }
// second rectangle
if (IsPointWithinRectangle(A1, B1, C1, D1, A0, false)) { match = true; }
if (IsPointWithinRectangle(A1, B1, C1, D1, B0, false)) { match = true; }
if (IsPointWithinRectangle(A1, B1, C1, D1, C0, false)) { match = true; }
if (IsPointWithinRectangle(A1, B1, C1, D1, D0, false)) { match = true; }

if (match)
return true;
else
return false;
}
public static bool IsPointWithinRectangle(Vector2 A, Vector2 B, Vector2 C, Vector2 D, Vector2 collision_point, bool reversewindingalsotrue)
{
int numberofplanescrossed = 0;
if (HasPointCrossedPlane2d(A, B, collision_point)) { numberofplanescrossed++; } else { numberofplanescrossed--; }
if (HasPointCrossedPlane2d(B, C, collision_point)) { numberofplanescrossed++; } else { numberofplanescrossed--; }
if (HasPointCrossedPlane2d(C, D, collision_point)) { numberofplanescrossed++; } else { numberofplanescrossed--; }
if (HasPointCrossedPlane2d(D, A, collision_point)) { numberofplanescrossed++; } else { numberofplanescrossed--; }
if ((reversewindingalsotrue == false && numberofplanescrossed >= 4) || (reversewindingalsotrue && numberofplanescrossed <= -4))
{ return true; }
else
{ return false; }
}
public static bool HasPointCrossedPlane2d(Vector2 start, Vector2 end, Vector2 collision_point)
{
Vector2 B = (end - start);
Vector2 A = (collision_point - start);
// We only need the signed result
// cross right and dot
float sign = A.X * -B.Y + A.Y * B.X;
if (sign > 0.0f)
return true;
else
return false;
}

public static Vector2 Rotate2dPointAboutOriginOnZaxis(Vector2 p, Vector2 o, double q)
{
//x' = x*cos s - y*sin s , y' = x*sin s + y*cos s
double x = p.X - o.X; // transform locally to the orgin
double y = p.Y - o.Y;
double rx = x * Math.Cos(q) - y * Math.Sin(q);
double ry = x * Math.Sin(q) + y * Math.Cos(q);
p.X = (float)rx + o.X; // translate back to non local
p.Y = (float)ry + o.Y;
return p;
}

public static void DrawCenteredRotatedRectangle(Texture2D textureobj, Rectangle screenrect, Rectangle texturerect, float rot, Color color)
{
// xna implicitly set the origin to the top left point of the rectangle.
// which i argued is not proper however it is made that way anyways.
// 0 0 should be the top left of the coordinate system not the local object origin.
// if your going to pick a arbitrary rotation origin and name it center put it in the center of the local object.
screenrect.X += (int)(screenrect.Width * .5f);
screenrect.Y += (int)(screenrect.Height * .5f);
Vector2 toff = new Vector2(texturerect.Width * .5f, texturerect.Height * .5f);
spriteBatch.Draw(textureobj, screenrect, texturerect, color, rot, toff, SpriteEffects.None, 0);
}

public static float Atan2Xna(float difx, float dify)
{
return (float)Math.Atan2(difx, dify) * -1;
}

public static float AlignRotation(float rotation)
{
if (rotation > ExampleHelperClass.PI2) { rotation -= ExampleHelperClass.PI2; }
if (rotation < 0f) { rotation += ExampleHelperClass.PI2; }
return rotation;
}

// visual version
public static bool IsPointWithinRectangleDisplay(Vector2 A, Vector2 B, Vector2 C, Vector2 D, Vector2 collision_point, bool reversewindingalsotrue)
{
int numberofplanescrossed = 0;
if (HasPointCrossedPlane2d(A, B, collision_point)) { DisplayRightCrossLine(A, B, collision_point, true); numberofplanescrossed++; } else { DisplayRightCrossLine(A, B, collision_point, false); numberofplanescrossed--; }
if (HasPointCrossedPlane2d(B, C, collision_point)) { DisplayRightCrossLine(B, C, collision_point, true); numberofplanescrossed++; } else { DisplayRightCrossLine(B, C, collision_point, false); numberofplanescrossed--; }
if (HasPointCrossedPlane2d(C, D, collision_point)) { DisplayRightCrossLine(C, D, collision_point, true); numberofplanescrossed++; } else { DisplayRightCrossLine(C, D, collision_point, false); numberofplanescrossed--; }
if (HasPointCrossedPlane2d(D, A, collision_point)) { DisplayRightCrossLine(D, A, collision_point, true); numberofplanescrossed++; } else { DisplayRightCrossLine(D, A, collision_point, false); numberofplanescrossed--; }
if ((reversewindingalsotrue == false && numberofplanescrossed >= 4) || (reversewindingalsotrue && numberofplanescrossed <= -4))
{ return true; }
else
{ return false; }
}
// visual
public static void DisplayRightCrossLine(Vector2 start, Vector2 end, Vector2 targetPosition, bool trueorfalse)
{
Vector2 B = (end - start);
Vector2 visualstart = (end - start) * .5f + start;
Vector2 visualNormal = new Vector2(-B.Y, B.X);
if (trueorfalse)
{
DrawBasicLine(visualstart, (.2f * visualNormal + visualstart), 1, Color.Red);
DrawBasicLine(visualstart, targetPosition, 1, Color.Red);
}
else
{
DrawBasicLine(visualstart, (.2f * visualNormal + visualstart), 1, Color.Green);
DrawBasicLine(visualstart, targetPosition, 1, Color.Green);
}
}
}``````
4 Likes

Can you show a 3D example?

This is way too cool to be missedâ€¦

A comparison with FPS between the other method and this might be handy for others to seeâ€¦

Good stuff!

Yes i can do a 3d example.

Itâ€™s probably simpler without all of spritebatchâ€™s annoying forced origin and translation stuff that you have to dodge.

but not today im a little tired.

Dunno if i really want to do the whole per pixel bitmap thing though sort of a waste of time to even compare the two a big picture with thousands of potential array access a rotation on each one. vs a % of the number of sign checks that can potentially be smartened down to just a few first to exclude a intersection.

Rotation in this example is not actually a part of the collision check its just in there to draw the lines and demonstrate the idea visually.

The heart of the 2d collision check is this method.

``````public static bool HasPointCrossedPlane2d(Vector2 start, Vector2 end, Vector2 collision_point)
{
Vector2 B = (end - start);
Vector2 A = (collision_point - start);
// We only need the signed result
// cross right and dot
float sign = A.X * -B.Y + A.Y * B.X;
if (sign > 0.0f)
return true;
else
return false;
}
``````

A vector3 version is basically the same.

Other
Then i canâ€™t combine the cross and dot in 3d as the z axis adds to many undefined possibility with different coordinate systems, so you do them back to back.

Vector3.Cross to get B
then get the sign of the Vector3.Dot(A,B)

were B is found from either 3 points (such as a 3d triangle) and the entered winding order.

``````    public static Vector3   CrossProduct3d(Vector3 a, Vector3 b, Vector3 c)
{
return new Vector3
(
((b.Y - a.Y) * (c.Z - b.Z)) - ((c.Y - b.Y) * (b.Z - a.Z)),
((b.Z - a.Z) * (c.X - b.X)) - ((c.Z - b.Z) * (b.X - a.X)),
((b.X - a.X) * (c.Y - b.Y)) - ((c.X - b.X) * (b.Y - a.Y))
);
}
``````

or how xna monogame does it from two normalized directions and the entered order.

rest of its the same pretty much.

A fully convex set of 3d planes has surface normals that forms a solid object. Most objects in 3d already have normals used for lighting which are usually the same thing as a cross products normal i.e. lighting normals, though not always, either way.
These are or can be created in the model itself. Such as a cube or pyramid but more complex objects can be broken up to form convex objects as well. Also not every triangle needs to be used as a surface. A bounding polyhedron can be approximated over many triangles much more accurately then a rectangle or sphere.

The drawback in 2d is you have to either make a editor or trace out points over a image in a clockwise fashion. Though itâ€™s possible to automate it completely i suppose.
There is no drawback really in 3d really. Some games use it to have a physical deflection and such off surfaces, (world of tanks) comes to mind and others were the reflect function can also be used against these surface cross products after a hit is registered.

Broad phase collision checks of course can still be used but for dead on surface checks were you need to know a bounce direction or angle of incidence or want to eliminate 10000 little box checks, its how its done.

1 Like