Develop Reference

Arc lines between 2 objects on a sphere Unity3D

I need a little help with maths for drawing lines between 2 points on a sphere. I have a 3d globe and some markers on it. I need to draw curved line from point 1 to point 2. I managed to draw lines from point to point with LineRenderer, but they are drawn with the wrong angle and I can't figure out, how to implement lines that go at the right angle. The code by far:
public static void DrawLine(Transform From, Transform To){
float count = 12f;
LineRenderer linerenderer;
GameObject line = new GameObject("Line");
linerenderer = line.AddComponent<LineRenderer>();
var points = new List<Vector3>();
Vector3 center = new Vector3(
(From.transform.position.x + To.transform.position.x) / 2f,
(From.transform.position.y + To.transform.position.y) ,
(From.transform.position.z + To.transform.position.z) / 2f
);
for (float ratio = 0; ratio <= 1; ratio += 1 / count)
{
var tangent1 = Vector3.Lerp(From.position, center, ratio);
var tangent2 = Vector3.Lerp(center, To.position, ratio);
var curve = Vector3.Lerp(tangent1, tangent2, ratio);
points.Add(curve);
}
linerenderer.positionCount = points.Count;
linerenderer.SetPositions(points.ToArray());
}
So what I have now is creepy lines rising above along y axis:
What should I take into account to let lines go along the sphere?

I suggest you to find the normal vector of your two points with a cross product (if your sphere is centered at the origin) and then normalize it to use it as a rotation axis for a rotation using quaternions. To make the interpolations, you can simply rotate the first point around this vector with an angle of k * a where k is a parameter from 0 to 1 and a is the angle between your first two vectors which you can find with the acos() of the dot product of your two normalized points
EDIT : I thought about a much easier solution (again, if the sphere is centered) : you can do a lerp between your two vectors and then normalize the result and multiply it by the radius of the sphere. However, the spacings between the resulting points wont be constant, especially if they are far from each other.
EDIT 2 : you can fix the problem of the second solution by using a function instead of a linear parameter for the lerp : f(t) = sin(t*a)/sin((PI+a*(1-2*t))/2)/dist(point1, point2) where a is the angle between the two points.

Get points x distance inside a polygon

I can't figure out a way to do this. I have a list of vector2 points and I need all the points which are inside that polygon with a x distance.
So I have a List of Green points and looking for a List of Red points that have a x distance from respective green points.
I am thinking of getting 2 imaginary points, 1 unity towards the previous and next point.
Then moving towards the center of that 2 points by x distance. But then if the inter angle is not 90 then it will move outside of the polygon.
Vector2 me = point; // point
Vector2 next = n_point; // on left
Vector2 previous = p_point; // on right
//Debug.DrawLine(me, (me - next), Color.green);
// 2 points ep1 & ep2
Vector2 center = Vector2.Lerp(ep1,ep2, 0.5f);
Vector2 finalpoint = Vector2.Lerp(me,center,0.1f); //move towards center
I think I am overthinking this. Is there a super-easy way to do this?

Assuming that all the edges are either horizontal or vertical I would simply consider each possible case separately.
Get the direction vectors.
Vector2 from = me - previous;
Vector2 to = next - me;
I also assume that there is always a turn. I.e., if from is horizontal, then to is vertical and vice versa. Either x or y is 0.0f and the other coordinate is not zero.
I also assume that the x-axis points to the right and the y-axis upwards.
Assuming points are listed clock-wise.
float x, y;
if (from.x > 0.0f) { // from points to the right
y = me.y - distance;
if (to.y > 0.0f) x = me.x + distance else x = me.x - distance;
} else if (from.x < 0.0f) { // from points to the left
y = me.y + distance;
if (to.y > 0.0f) x = me.x + distance else x = me.x - distance;
} else if (from.y > 0.0f) { // from points upwards
x = me.x + distance;
if (to.x > 0.0f) y = me.y - distance else y = me.y + distance;
} else { // from.y < 0.0f, points downwards
x = me.x - distance;
if (to.x > 0.0f) y = me.y - distance else y = me.y + distance;
}
Vector2 me_inner = new Vector2(x, y);
I hope I got all the signs right.

There are two methods that spring to mind
Option1:
For each line define a normal, i.e. a perpendicular line pointing outward
Define a normal for each vertex as the average of the normals of the lines the vertex is part of.
Move the vertex X units along the normal.
This is fairly easy to implement, but may have problems with self-intersection for some kinds of geometry.
Option2:
For each line define a normal, i.e. a perpendicular line pointing outward
Move each line-segment X Units along the normal.
for each sequential pair of line segments determine if:
the two line segments intersect, if so, use the intersection point as the vertex. i.e. add the intersection point into your point-list.
If they do not intersect, insert a new line segment between the start and end point of the lines. i.e. Insert both start and end vertex to your point-list.
This should handle self-intersection better, but there might still be problem-cases. And it a bit more cumbersome to implement. It somewhat depend on how exact you need the new line positioned, and well it should handle different kinds of geometry.

AABB vs Circle collision in custom physics engine

I have followed this tutorial: https://gamedevelopment.tutsplus.com/tutorials/how-to-create-a-custom-2d-physics-engine-the-basics-and-impulse-resolution--gamedev-6331 to create a 2d physics engine in c# (he works in almost all the time wrong and inconsistent pseudo c++) I've got Circle vs Circle collision and AABB vs AABB collision working fine. But when trying the AABB vs Circle collison (below) the two rigidbodies just stick together and slowly move glitchy in one direction.
I would be super thankful if someone could help me with this as I have spent days and still don't know what's causing the error.
If someone needs more information from my code, I'd be happy to provide it.
public static bool AABBvsCircle(ref Collision result) {
RigidBody AABB = result.a.Shape is AABB ? result.a : result.b;
RigidBody CIRCLE = result.b.Shape is Circle ? result.b : result.a;
Vector2 n = CIRCLE.Position - AABB.Position;
Vector2 closest = n;
float x_extent = ((AABB)AABB.Shape).HalfWidth;
float y_extent = ((AABB)AABB.Shape).HalfHeight;
closest.X = Clamp(-x_extent, x_extent, closest.X);
closest.Y = Clamp(-y_extent, y_extent, closest.Y);
bool inside = false;
if (n == closest) {
inside = true;
if (Abs(n.X) > Abs(n.Y)) {
// Clamp to closest extent
if (closest.X > 0)
closest.X = x_extent;
else
closest.X = -x_extent;
}
// y axis is shorter
else {
// Clamp to closest extent
if (closest.Y > 0)
closest.Y = y_extent;
else
closest.Y = -y_extent;
}
}
Vector2 normal = n - closest;
float d = normal.LengthSquared();
float r = ((Circle)CIRCLE.Shape).Radius;
// Early out of the radius is shorter than distance to closest point and
// Circle not inside the AABB
if (d > (r * r) && !inside)
return false;
// Avoided sqrt until we needed
d = (float)Sqrt(d);
if (inside) {
result.normal = -normal / d;
result.penetration = r - d;
}
else {
result.normal = normal / d;
result.penetration = r - d;
}
return true;
}
edit 1 collison resolution method in "Collision" struct
public void Resolve() {
Vector2 rv = b.Velocity - a.Velocity;
float velAlongNormal = Vector2.Dot(rv, normal);
if (velAlongNormal > 0)
return;
float e = Min(a.Restitution, b.Restitution);
float j = -(1 + e) * velAlongNormal;
j /= a.InvertedMass + b.InvertedMass;
Vector2 impulse = j * normal;
a.Velocity -= a.InvertedMass * impulse;
b.Velocity += b.InvertedMass * impulse;
const float percent = 0.2f; // usually 20% to 80%
const float slop = 0.01f; // usually 0.01 to 0.1
Vector2 correction = Max(penetration - slop, 0.0f) / (a.InvertedMass + b.InvertedMass) * percent * normal;
if (float.IsNaN(correction.X) || float.IsNaN(correction.Y))
correction = Vector2.Zero;
a.Position -= a.InvertedMass * correction;
b.Position += b.InvertedMass * correction;
}

Before doing any detailed examining of the code logic, I spotted this potential mistake:
result.normal = -normal / d;
Since d was set to normal.LengthSquared and not normal.Length as it should be, the applied position correction could either be (much) smaller or (much) bigger than intended. Given that your objects are "sticking together", it is likely to be the former, i.e. d > 1.
(The fix is of course simply result.normal = -normal / Math.Sqrt(d);)
Note that the above may not be the only source of error; let me know if there is still undesirable behavior.

Although your tag specifies C#; here are basic AABB to AABB & AABB to Circle collisions that are done in C++ as these are take from: LernOpenGL:InPractice:2DGame : Collision Detection
AABB - AABB Collsion
// AABB to AABB Collision
GLboolean CheckCollision(GameObject &one, GameObject &two) {
// Collision x-axis?
bool collisionX = one.Position.x + one.Size.x >= two.Position.x &&
two.Position.x + two.Size.x >= one.Position.x;
// Collision y-axis?
bool collisionY = one.Position.y + one.Size.y >= two.Position.y &&
two.Position.y + two.Size.y >= one.Position.y;
// Collision only if on both axes
return collisionX && collisionY;
}
AABB To Circle Collision Without Resolution
// AABB to Circle Collision without Resolution
GLboolean CheckCollision(BallObject &one, GameObject &two) {
// Get center point circle first
glm::vec2 center(one.Position + one.Radius);
// Calculate AABB info (center, half-extents)
glm::vec2 aabb_half_extents(two.Size.x / 2, two.Size.y / 2);
glm::vec2 aabb_center(
two.Position.x + aabb_half_extents.x,
two.Position.y + aabb_half_extents.y
);
// Get difference vector between both centers
glm::vec2 difference = center - aabb_center;
glm::vec2 clamped = glm::clamp(difference, -aabb_half_extents, aabb_half_extents);
// Add clamped value to AABB_center and we get the value of box closest to circle
glm::vec2 closest = aabb_center + clamped;
// Retrieve vector between center circle and closest point AABB and check if length <= radius
difference = closest - center;
return glm::length(difference) < one.Radius;
}
Then in the next section of his online tutorial he shows how to do Collision Resolution using the above method found here: LearnOpenGL : Collision Resolution
In this section he adds an enumeration, another function and an std::tuple<> to refine the above detection system while trying to keep the code easier & cleaner to manage and read.
enum Direction {
UP,
RIGHT,
DOWN,
LEFT
};
Direction VectorDirection(glm::vec2 target)
{
glm::vec2 compass[] = {
glm::vec2(0.0f, 1.0f), // up
glm::vec2(1.0f, 0.0f), // right
glm::vec2(0.0f, -1.0f), // down
glm::vec2(-1.0f, 0.0f) // left
};
GLfloat max = 0.0f;
GLuint best_match = -1;
for (GLuint i = 0; i < 4; i++)
{
GLfloat dot_product = glm::dot(glm::normalize(target), compass[i]);
if (dot_product > max)
{
max = dot_product;
best_match = i;
}
}
return (Direction)best_match;
}
typedef std::tuple<GLboolean, Direction, glm::vec2> Collision;
However there is a slight change to the original CheckCollsion() function for AABB to Circle by changing its declaration/definition to return a Collision instead of a GLboolean.
AABB - Circle Collision With Collision Resolution
// AABB - Circle Collision with Collision Resolution
Collision CheckCollision(BallObject &one, GameObject &two) {
// Get center point circle first
glm::vec2 center(one.Position + one.Radius);
// Calculate AABB info (center, half-extents)
glm::vec2 aabb_half_extents(two.Size.x / 2, two.Size.y / 2);
glm::vec2 aabb_center(two.Position.x + aabb_half_extents.x, two.Position.y + aabb_half_extents.y);
// Get difference vector between both centers
glm::vec2 difference = center - aabb_center;
glm::vec2 clamped = glm::clamp(difference, -aabb_half_extents, aabb_half_extents);
// Now that we know the the clamped values, add this to AABB_center and we get the value of box closest to circle
glm::vec2 closest = aabb_center + clamped;
// Now retrieve vector between center circle and closest point AABB and check if length < radius
difference = closest - center;
if (glm::length(difference) < one.Radius) // not <= since in that case a collision also occurs when object one exactly touches object two, which they are at the end of each collision resolution stage.
return std::make_tuple(GL_TRUE, VectorDirection(difference), difference);
else
return std::make_tuple(GL_FALSE, UP, glm::vec2(0, 0));
}
Where the above functions or methods are called within this function that does the actually logic if a collision is detected.
void Game::DoCollisions()
{
for (GameObject &box : this->Levels[this->Level].Bricks)
{
if (!box.Destroyed)
{
Collision collision = CheckCollision(*Ball, box);
if (std::get<0>(collision)) // If collision is true
{
// Destroy block if not solid
if (!box.IsSolid)
box.Destroyed = GL_TRUE;
// Collision resolution
Direction dir = std::get<1>(collision);
glm::vec2 diff_vector = std::get<2>(collision);
if (dir == LEFT || dir == RIGHT) // Horizontal collision
{
Ball->Velocity.x = -Ball->Velocity.x; // Reverse horizontal velocity
// Relocate
GLfloat penetration = Ball->Radius - std::abs(diff_vector.x);
if (dir == LEFT)
Ball->Position.x += penetration; // Move ball to right
else
Ball->Position.x -= penetration; // Move ball to left;
}
else // Vertical collision
{
Ball->Velocity.y = -Ball->Velocity.y; // Reverse vertical velocity
// Relocate
GLfloat penetration = Ball->Radius - std::abs(diff_vector.y);
if (dir == UP)
Ball->Position.y -= penetration; // Move ball bback up
else
Ball->Position.y += penetration; // Move ball back down
}
}
}
}
// Also check collisions for player pad (unless stuck)
Collision result = CheckCollision(*Ball, *Player);
if (!Ball->Stuck && std::get<0>(result))
{
// Check where it hit the board, and change velocity based on where it hit the board
GLfloat centerBoard = Player->Position.x + Player->Size.x / 2;
GLfloat distance = (Ball->Position.x + Ball->Radius) - centerBoard;
GLfloat percentage = distance / (Player->Size.x / 2);
// Then move accordingly
GLfloat strength = 2.0f;
glm::vec2 oldVelocity = Ball->Velocity;
Ball->Velocity.x = INITIAL_BALL_VELOCITY.x * percentage * strength;
//Ball->Velocity.y = -Ball->Velocity.y;
Ball->Velocity = glm::normalize(Ball->Velocity) * glm::length(oldVelocity); // Keep speed consistent over both axes (multiply by length of old velocity, so total strength is not changed)
// Fix sticky paddle
Ball->Velocity.y = -1 * abs(Ball->Velocity.y);
}
}
Now some of the code above is GameSpecific as in the Game class, Ball class, Player etc. where these are considered and inherited from a GameObject, but the algorithm itself should provide useful as this is exactly what you are looking for but from a different language. Now as to your actually problem it appears you are using more than basic motion as it appears you are using some form of kinetics that can be seen from your Resolve() method.
The overall Pseudo Algorithm for doing AABB to Circle Collision with Resolution would be as follows:
Do Collisions:
Check For Collision: Ball With Box
Get Center Point Of Circle First
Calculate AABB Info (Center & Half-Extents)
Get Difference Vector Between Both Centers
Clamp That Difference Between The [-Half-Extents, Half-Extents]
Add The Clamped Value To The AABB-Center To Give The Point Of Box Closest To The Circle
Retrieve & Return The Vector Between Center Circle & Closest Point AABB & Check If Length Is < Radius (In this case a Collision).
If True Return tuple(GL_TRUE, VectorDirection(difference), difference))
See Function Above For VectorDirection Implementation.
Else Return tuple(GL_FALSE, UP, glm::vec2(0,0))
Perform Collision Resolution (Test If Collision Is True)
Extract Direction & Difference Vector
Test Direction For Horizontal Collision
If True Reverse Horizontal Velocity
Get Penetration Amount (Ball Radius - abs(diff_vector.x))
Test If Direction Is Left Or Right (W,E)
If Left - Move Ball To Right (ball.position.x += penetration)
Else Right - Move Ball To Left (ball.position.x -= penetration)
Else Test Direction For Vertical Collision
If True Reverse Vertical Velocity
Get Penetration Amount (Ball Radius - abs(diff_vector.y))
Test If Direction Is Up Or Down (N,S)
If Up - Move Ball Up (ball.position.y -= penetration)
Else Down - Move Ball Down (ball.position.y += penetration)
Now the above algorithm shown assumes that the boxes are not rotated and that their top & bottom edges are parallel with the horizontal and that their sides are parallel with the left and right edges of the window-screen coordinates. Also in the bottom section with the vertical displacement this also assumes that the top left corner of the screen - the first pixel is (0,0), thus the opposite operation for vertical displacement. This also assumes 2D collisions and not 3D Ridged or Ragdoll type collisions. You can use this to compare against your own source - implementation, but as far as just looking at your code without running it through a debugger it is extremely hard for me to see or find out what is actually causing your bug. I hope this provides you with the help that you need.
The above code from the mentioned OpenGL tutorial website does work as I have tested it myself. This algorithm is of the simplest of collision detections and is by far no means a comprehensive system and it still has caveats or pitfalls not mentioned here, but does suffice for the application it was used in. If you need more information about Collision Detections there is a few chapters that can be read in Ian Millington's book Game Physics Engine Development Although his book is based on a generalized 3D Physics Engine and only briefly discuses Collision Detection as their are full Books dedicated to the growing popularity of such complex beasts.

C# XNA Calculate distance between rectangles (rotation-friendly)

Here's 2 methods available;
if(rectangle.Intersects(otherRectangle))
{
//collision stuff
}
Catch: Only works with non-rotating rectangles.
if(Vector2.Distance(player.pos, enemy.pos) < 50)
{
//collision stuff
}
Catch: Only works with circles.
What I want is to calculate x and y in this image:
Facts
The width and length of both rectangles is defined, along with their rotations.
I can calculate D using the Pythagorean theorem.
But the TRUE distance is D - (X + Y).
General approach
Evidently x and y can be calculated using the Cosine rule.
But I only have the width or length and the angle between the two shapes.
Complication
Plus, this needs to work for any rotation.
The rectangle on the left could be rotated in any direction, and x would be different depending on said rotation.
Question
How would I calculate x and y?
I just want an effective collision detection method more complex than bounding boxes and Pythagoras' theorem.

One approach is to rotate the line with the inverse angle and check with the axis-aligned box:
class RotatedBox
{
...
float CalcIntersectionLength(Vector2 lineTo) //assume that the line starts at the box' origin
{
Matrix myTransform = Matrix.CreateRotationZ(-this.RotationAngle);
var lineDirection = Vector2.Transform(lineTo -this.Center, myTransform);
lineDirection.Normalize();
var distanceToHitLeftOrRight = this.Width / 2 / Math.Abs(lineDirection.X);
var distanceToHitTopOrBottom = this.Height / 2 / Math.Abbs(lineDirection.Y);
return Math.Min(distanceToHitLeftOrRight, distanceToHitTopOrBottom);
}
}
Now you can calculate the actual distance with
var distance = (box1.Center - box2.Center).Length
- box1.CalcIntersectionLength(box2.Center)
- box2.CalcIntersectionLength(box1.Center);
Be sure that the rotation direction matches your visualization.

C# / XNA - 2D collision engine glitch?

I've got quite a lot of code here, but it's relatively straightforward.
This is all snippets from different classes, all references are right, but I think I've done a math-based error somewhere and I can't find it. It always finds a collision on the y axis a pixel before it should. I haven't tried it with different X axis positions but it seems to fall past blocks next to it fine.
The struct "mapSection" just contains two Vector2s- A top-left block and bottom-left block coordinate.
tileManager.def_ts is the default tile width and height (32). The player's size is 32x64.
The toWorldSpace function does nothing right now other than return so that's not the problem.
When I say block coordinate I mean which index the block is in the tile array (Ex 0, 0 is the first block, 0, 1 is the second block on the Y axis, 1, 3 is 1 block in on the X axis and 3 on the Y axis, I do not mean actual pixels.)
From tile engine class:
public mapSection toMapMinMax(Vector2 position, Vector2 size)
{
position = toWorldSpace(position);
position.X = (float)Math.Floor(position.X / tileManager.def_ts);
position.Y = (float)Math.Floor(position.Y / tileManager.def_ts);
size.X = (float)Math.Floor(size.X / tileManager.def_ts);
size.Y = (float)Math.Floor(size.Y / tileManager.def_ts);
return new mapSection(position, position + size);
}
public bool collision(Vector2 screenPosition, Vector2 size)
{
mapSection mapCollisionPossibilities = toMapMinMax(screenPosition, size);
for (int y = (int)mapCollisionPossibilities.topLeft.Y; y <= mapCollisionPossibilities.bottomRight.Y; y++)
{
for (int x = (int)mapCollisionPossibilities.topLeft.X; x <= mapCollisionPossibilities.bottomRight.X; x++)
{
if (x >= 0 && y >= 0 && y < tiles.Count && x < tiles[y].Count)
{
if (tileManager.tileTypes[tiles[y][x]].collideable == true)
{
return true;
}
}
}
}
return false;
}
And this is the code from the player class:
if (!tEngine.collision(position + new Vector2(0, 1), new Vector2(32, 64)))
{
position.Y += 1;
}
I add "Vector2(0, 1)" because I want to see if there's a collision a pixel further down; so that he falls until he hits something. It's very basic right now but it's only to test the collision engine, which isn't working.
There's a picture of the error. You can see the player is a pixel too high.
In the picture, "X:" is the top-left block coordinate on X axis, "X2:" is the bottom-right block coordinate on the X axis, and same with "Y:" and "Y2: except Y axis. They're read from the mapSection directly.
If anyone can notice why this is happening, it would be massively appreciated.
Thanks.
If you cannot understand any section of the code just post in the comments and I'll be happy to explain, or if you think I've been a bit too unspecific in some area of this post.

EDIT: For the tile coordinates issue, your toMapMinMax code should be more like this:
EDIT2: have subtracted (1, 1) from bottomRight, since it is a size we are adding.
public mapSection toMapMinMax(Vector2 position, Vector2 size)
{
Vector2 topLeft = position;
Vector2 bottomRight = position + size - new Vector2(1, 1);
topLeft.X = (float)Math.Floor(topLeft.X / tileManager.def_ts);
topLeft.Y = (float)Math.Floor(topLeft.Y / tileManager.def_ts);
bottomRight.X = (float)Math.Floor(bottomRight.X / tileManager.def_ts);
bottomRight.Y = (float)Math.Floor(bottomRight.Y / tileManager.def_ts);
return new mapSection(topLeft, bottomRight);
}
Also, I was wrong in my above comment; you do want <= signs in your two for loops, because most of the time you will be checking 6 tiles.
for the off-by-one-pixel issue:
In order for you to see the character off by some amount of pixels, the draw code and the collision code must be different. If they were identical, for example if they were both off by 15 pixels (you collide 15 pixels too early, but you are also drawing 15 pixels ahead), you wouldn't see any change.
The 1 pixel gap indicates a 1 pixel difference between the draw coordinate calculation and the collision coordinate calculation. This 1 pixel difference is most likely caused by differences in rounding, probably that you are calling Math.Floor in the collision code, but are not rounding the coordinates in the draw code. (I would guess you are probably just passing the position Vector2 straight to the SpriteBatch.Draw method).