In the above Image there are two Cubes with a Rigidbody and a BoxCollider attached to each of them. Let's say we have an animation in which the cube on top moves and overlaps the cube which is below it. The Cube on top moves some distance on y-axis and the cube below doesn't move. How do I calculate the yellow area,i.e, the area which shows overlapping?
Thank You.
Assuming these are always cubes and world axis aligned you could probably simply do
public Vector3 OverlapArea(BoxCollider a, BoxCollider b)
{
// get the bounds of both colliders
var boundsA = a.bounds;
var boundsB = b.bounds;
// first heck whether the two objects are even overlapping at all
if(!boundsA.Intersects(boundsB))
{
Vector3.zero;
}
// now that we know they at least overlap somehow we can calculate
// get the bounds of both colliders
var boundsA = a.bounds;
var boundsB = b.bounds;
// get min and max point of both
var minA = boundsA.min; (basically the bottom-left-back corner point)
var maxA = boundsA.max; (basically the top-right-front corner point)
var minB = boundsB.min;
var maxB = boundsB.max;
// we want the smaller of the max and the higher of the min points
var lowerMax = new Vector3.Min(maxA, maxB);
var higherMin = new Vector3.Max(minA, minB);
// the delta between those is now your overlapping area
return lowerMax - higherMin;
}
and if you want the area in m³ as usual just do
var overlap = OverlapArea(colliderA, colliderB);
var overlapArea = overlap.x * overlap.y * overlap.z;
See
Collider.bounds
Bounds.Intersects
Bounds.min / Bounds.max
Vector3.Min / Vector3.Max
Anything beyond that (rotated and differently shaped objects) would probably fit better for the Mathematics community
Related
I built a 3D Chess game which works flawlessly. But I would like to make some changes to the movement.
The piece is supposed to walk a number of tiles. For example with a range of 3 it can either move 3 to one direction (left for example), or 2 left 1 up/down, or 1 left 2 up/down.
Which minor change do I have to implement in my code for it to work?
private Vector2Int[] directions = new Vector2Int[]
{
Vector2Int.left,
Vector2Int.up,
Vector2Int.right,
Vector2Int.down,
new Vector2Int(1, 1),
new Vector2Int(1, -1),
new Vector2Int(-1, 1),
new Vector2Int(-1,- 1),
};
public override List<Vector2Int> SelectAvaliableSquares()
{
avaliableMoves.Clear();
float range = Board.BOARD_SIZE;
foreach (var direction in directions)
{
for (int i = 1; i <= range; i++)
{
Vector2Int nextCoords = occupiedSquare + direction * i;
Piece piece = board.GetPieceOnSquare(nextCoords);
if (!board.CheckIfCoordinatesAreOnBoard(nextCoords))
break;
if (piece == null)
TryToAddMove(nextCoords);
else if (!piece.IsFromSameTeam(this))
{
TryToAddMove(nextCoords);
break;
}
else if (piece.IsFromSameTeam(this))
break;
}
}
return avaliableMoves;
}
The given code is an example of the movement of an ordinary queen.
Added a picture to demonstrate the movement.
enter image description here
Find the center of each chess tile and hold them all in a 2D array. Calculate which tiles the unit must traverse in accordance with its type and location. Then when you move, have it move first along the X axis and then the Y axis or vice versa. If it moves diagonally just move along both axes at the same time.
I've been programming an ability for a Hack n Slash which needs to check Units within a pie slice (or inbetween two angles with max length). But I'm stuck on how to check whether an unit is within the arc.
Scenario (Not enough, rep for an image sorry im new)
I currently use Physics2D.OverlapSphere() to get all of the objects within the maximum range. I then loop through all of the found objects to see whether they are within the two angles I specify. Yet this has janky results, probably because angles don't like negative values and value above 360.
How could I make this work or is there a better way to do this?
I probably need to change the way I check whether the angle is within the bounds.
Thanks in advance guys! I might respond with some delay as I won't be at my laptop for a couple hours.
Here is the code snippet:
public static List<EntityBase> GetEntitiesInArc(Vector2 startPosition, float angle, float angularWidth, float radius)
{
var colliders = Physics2D.OverlapCircleAll(startPosition, radius, 1 << LayerMask.NameToLayer("Entity"));
var targetList = new List<EntityBase>();
var left = angle - angularWidth / 2f;
var right = angle + angularWidth / 2f;
foreach (var possibleTarget in colliders)
{
if (possibleTarget.GetComponent<EntityBase>())
{
var possibleTargetAngle = Vector2.Angle(startPosition, possibleTarget.transform.position);
if (possibleTargetAngle >= left && possibleTargetAngle <= right)
{
targetList.Add(possibleTarget.GetComponent<EntityBase>());
}
}
}
return targetList;
}
Vector2.Angle(startPosition, possibleTarget.transform.position);
This is wrong. Imagine a line from the scene origin (0,0) to startPosition and a line to the transform.position. Vector2.Angle is giving you the angle between those two lines, which is not what you want to measure.
What you actually want is to give GetEntitiesInArc a forward vector then get the vector from the origin to the target position (var directionToTarget = startPosition - possibleTarget.transform.position) and measure Vector2.Angle(forward, directionToTarget).
I have a point in space represented by a 4x4 matrix. I'd like to get the screen coordinates for the point. Picking appears to be the exact opposite fo what I need. I'm using the screen coordinate to determine where to draw text.
Currently the text I draw is floating in space far in front of the points. I've attached a screenshot of zoomed-in and zoomed-out to better explain. As you can see in the screenshot, the distance between each point is the same when zoomed in, when it should be smaller.
Am I missing a transformation? World coordinates consider 0,0,0 to be the center of the grid. I'm using SlimDX.
var viewProj = mMainCamera.View * mMainCamera.Projection;
//Convert 4x4 matrix for point to Vector4
var originalXyz = Vector3.Transform(Vector3.Zero, matrix);
//Vector4 to Vector3
Vector3 worldSpaceCoordinates = new Vector3(originalXyz.X, originalXyz.Y, originalXyz.Z);
//Transform point by view projection matrix
var transformedCoords = Vector3.Transform(worldSpaceCoordinates, viewProj);
Vector3 clipSpaceCoordinates = new Vector3(transformedCoords.X, transformedCoords.Y, transformedCoords.Z);
Vector2 pixelPosition = new Vector2((float)(0.5 * (clipSpaceCoordinates.X + 1) * ActualWidth), (float)(0.5 * (clipSpaceCoordinates.Y + 1) * ActualHeight));
Turns out I was way overthinking this. Just project the point to the screen by passing Vector3.Project your viewport information. It's a 3 line solution.
var viewProj = mMainCamera.View * mMainCamera.Projection;
var vp = mDevice.ImmediateContext.Rasterizer.GetViewports()[0];
var screenCoords = Vector3.Project(worldSpaceCoordinates, vp.X, vp.Y, vp.Width, vp.Height, vp.MinZ, vp.MaxZ, viewProj);
I'm currently making a 3D car game using XNA 3.1. It is a taxi game. So my main vehicle encounters traffic vehicles during the game. I'm having problems with coding the collision detection among traffic vehicles and the main vehicle. I used the bounding box method instead of bounding sphere method because bounding spheres don't cover the vehicles properly.
Below is the code i used to achieve collision. Problem with it is when the vehicle turns left or right bounding box doesn't change according to that.
I wrote this code in the update method.
carWorld = Matrix.CreateScale(1f) * Matrix.CreateTranslation(vehicalClassObs[0].Position);
trafficWorld = Matrix.CreateScale(1f) * Matrix.CreateTranslation(carObject.Position);
BoundingBox b=CalculateBoundingBox(carO);
BoundingBox c=CalculateBoundingBox(car);
Vector3[] obb = new Vector3[8];
b.GetCorners(obb);
Vector3.Transform(obb, ref carWorld, obb);
BoundingBox worldAABB = BoundingBox.CreateFromPoints(obb);
Vector3[] occ=new Vector3[8];
c.GetCorners(occ);
Vector3.Transform(occ, ref trafficWorld, occ);
BoundingBox worldAACC = BoundingBox.CreateFromPoints(occ);
if (worldAABB.Intersects(worldAACC))
col = true;
else col = false;
Below is the CalculateBoundingBox method
public BoundingBox CalculateBoundingBox(Model m_model)
{
// Create variables to hold min and max xyz values for the model. Initialise them to extremes
Vector3 modelMax = new Vector3(float.MinValue, float.MinValue, float.MinValue);
Vector3 modelMin = new Vector3(float.MaxValue, float.MaxValue, float.MaxValue);
foreach (ModelMesh mesh in m_model.Meshes)
{
Matrix[] m_transforms = new Matrix[m_model.Bones.Count];
m_model.CopyAbsoluteBoneTransformsTo(m_transforms);
//Create variables to hold min and max xyz values for the mesh. Initialise them to extremes
Vector3 meshMax = new Vector3(float.MinValue, float.MinValue, float.MinValue);
Vector3 meshMin = new Vector3(float.MaxValue, float.MaxValue, float.MaxValue);
// There may be multiple parts in a mesh (different materials etc.) so loop through each
foreach (ModelMeshPart part in mesh.MeshParts)
{
// The stride is how big, in bytes, one vertex is in the vertex buffer
// We have to use this as we do not know the make up of the vertex
int stride = part.VertexDeclaration.GetVertexStrideSize(0);
byte[] vertexData = new byte[stride * part.NumVertices];
mesh.VertexBuffer.GetData(part.BaseVertex * stride, vertexData, 0, part.NumVertices, 1); // fixed 13/4/11
// Find minimum and maximum xyz values for this mesh part
// We know the position will always be the first 3 float values of the vertex data
Vector3 vertPosition=new Vector3();
for (int ndx = 0; ndx < vertexData.Length; ndx += stride)
{
vertPosition.X= BitConverter.ToSingle(vertexData, ndx);
vertPosition.Y = BitConverter.ToSingle(vertexData, ndx + sizeof(float));
vertPosition.Z= BitConverter.ToSingle(vertexData, ndx + sizeof(float)*2);
// update our running values from this vertex
meshMin = Vector3.Min(meshMin, vertPosition);
meshMax = Vector3.Max(meshMax, vertPosition);
}
}
// transform by mesh bone transforms
meshMin = Vector3.Transform(meshMin, m_transforms[mesh.ParentBone.Index]);
meshMax = Vector3.Transform(meshMax, m_transforms[mesh.ParentBone.Index]);
// Expand model extents by the ones from this mesh
modelMin = Vector3.Min(modelMin, meshMin);
modelMax = Vector3.Max(modelMax, meshMax);
}
// Create and return the model bounding box
return new BoundingBox(modelMin, modelMax);
}
If someone can help me to solve this problem it wil be very helpful. If there is a better way to achieve collision other than the way i used please let me know about that method.
You have a couple of options here. The easiest is to transform the vehicle's bounding box according to the vehicle's world transforms (no projection or view required here since you're not concerned about camera position when checking for collisions.)
Assuming you already have the vehicle's original bounding box,
/// <summary>
/// Transforms a bounding box for collision detection
/// </summary>
/// <param name="vehicleBounds">Original, object-centered bounding box that contains a car model</param>
/// <param name="vehicleWorldMatrix">Vehicle's world transformation matrix (does not include projection or view)</param>
/// <returns>An axis-aligned bounding box (AABB) that will com </returns>
protected BoundingBox TransformBoundingBox(BoundingBox vehicleBounds, Matrix vehicleWorldMatrix)
{
var vertices = vehicleBounds.GetCorners();
/// get a couple of vertices to hold the outer bounds of the transformed bounding box.
var minVertex = new Vector3(float.MaxValue);
var maxVertex = new Vector3(float.MinValue);
for(int i=0;i<vertices.Length;i++)
{
var transformedVertex = Vector3.Transform(vertices[i],vehicleWorldMatrix);
/// update min and max with the component-wise minimum of each transformed vertex
/// to find the outer limits fo teh transformed bounding box
minVertex = Vector3.Min(minVertex, transformedVertex);
maxVertex = Vector3.Max(maxVertex, transformedVertex);
}
var result = new BoundingBox(minVertex, maxVertex);
return result;
}
For each vehicle, use that method to create a temporary bounding box to use for collisions. Only test transformed bounding boxes against each other, and do not overwrite you're original bounding box as you'll need to recalculate this box from your source any time the vehicle moves.
If you're using a multi-mesh model, use BoundingBox.CreateMerged() to combine them to get a box that contains the entire model, or perform your collisions for each sub-mesh bounding box (though this can get expensive without using some sort of acceleration structure).
What I have been using is a very simple method which can fit almost any situation. Here it is:
//Create one of the matricies
//Vector3 loc = new Vector3(0, 0, 0); //Wherever the model is.
//Matrix world1 = Matrix.CreateTransform(loc);
private bool IsCollision(Model model1, Matrix world1, Model model2, Matrix world2)
{
for (int meshIndex1 = 0; meshIndex1 < model1.Meshes.Count; meshIndex1++)
{
BoundingSphere sphere1 = model1.Meshes[meshIndex1].BoundingSphere;
sphere1 = sphere1.Transform(world1);
for (int meshIndex2 = 0; meshIndex2 < model2.Meshes.Count; meshIndex2++)
{
BoundingSphere sphere2 = model2.Meshes[meshIndex2].BoundingSphere;
sphere2 = sphere2.Transform(world2);
if (sphere1.Intersects(sphere2))
return true;
}
}
return false;
}
You can change all the spheres to boxes, but this might work. Additionally, what I do is move the location one axis at a time (X axis then Y axis then Z axis). This creates smoother collision.
I would like to understand how to measure the distance between two 3D objects, let's call them a parent object and a child object. Think of the parent as the body of a car and the child being a wheel of the car.
I understand how to get the difference based on the objects position in world space but I would like to get the difference as a measurement based on the parents relative object space.
E.g if the parent is facing East and the child is 2X, 3Y from the parent, measured in a relative sense. Such that if the parent rotated 60 degrees, the relative location of the child remains at a distance of 2x, 3y in the object space. Where as in a world space sense the child objects measurement as a Vector3 would be quite different.
Basically I just want a predictable way to get the difference so that a child object which is on the right of the patent can always stay right of the parent object.
This is the parent component, this update is run every frame:
[Serializable]
public class Component_Parent : BaseComponentAutoSerialization<ISceneEntity>
{
public override void OnUpdate(GameTime gameTime)
{
PassThrough.ParentMatrix = ParentObject.World;
PassThrough.ParentTranslation = ParentObject.World.Translation;
}
}
This next part is the child component:
[Serializable]
public class Component_Child : BaseComponentAutoSerialization<ISceneEntity>
{
Vector3 _parentOffset;
Quaternion _parentQuaternionOffset;
public override void OnUpdate(GameTime gameTime)
{
// Get a sceneobject from the ParentObject
SceneObject sceneobject = (SceneObject)ParentObject;
// This relies on the position never being at 0,0,0 for setup, so please don't do that
// or change it with more look ups so that you don't need to rely on a Zero Vector3 :-)
if (PassThrough.GroupSetupMode || _parentOffset == Vector3.Zero)
{
if (PassThrough.ParentTranslation != Vector3.Zero)
{
_parentOffset = sceneobject.World.Translation - PassThrough.ParentTranslation;
// Decompose World Matrix (Parent)
Quaternion parentQ = new Quaternion();
Vector3 parentSpot = new Vector3();
Vector3 parentScale = new Vector3();
PassThrough.ParentMatrix.Decompose(out parentScale, out parentQ, out parentSpot);
Matrix identity = Matrix.Identity;
// Decompose Identity Matrix (Parent)
Quaternion identityQ = new Quaternion();
Vector3 identitySpot = new Vector3();
Vector3 identityScale = new Vector3();
identity.Decompose(out identityScale, out identityQ, out identitySpot);
_parentQuaternionOffset = identityQ - parentQ;
}
}
else
{
if (_parentOffset != Vector3.Zero)
{
// Decompose World Matrix (Child)
Quaternion rotationQ = new Quaternion();
Vector3 spot = new Vector3();
Vector3 scale = new Vector3();
sceneobject.World.Decompose(out scale, out rotationQ, out spot);
// Decompose World Matrix (Parent)
Quaternion parentQ = new Quaternion();
Vector3 parentSpot = new Vector3();
Vector3 parentScale = new Vector3();
PassThrough.ParentMatrix.Decompose(out parentScale, out parentQ, out parentSpot);
Matrix location = Matrix.CreateTranslation(PassThrough.ParentTranslation);
Matrix rotation = Matrix.CreateFromQuaternion(parentQ);
Matrix rotation2 = Matrix.CreateFromQuaternion(_parentQuaternionOffset);
Matrix newWorld = rotation * location;
Vector3 testTranslation = newWorld.Translation + ((newWorld.Left * _parentOffset.X) + (newWorld.Up * _parentOffset.Y) + (newWorld.Forward * _parentOffset.Z));
Matrix scaleM = Matrix.CreateScale(scale);
//sceneobject.World = scaleM * (rotation * (Matrix.CreateTranslation(testTranslation)));
sceneobject.World = (Matrix.CreateTranslation(testTranslation));
}
}
}
}
I think it has something to do with keeping track of an offset rotation, from the identity matrix and I have started trying to add some code to that effect but really unsure of what next now.
Additional:
If I have the parent object facing the direction of the world space it all works, if it's facing a different direction then it's an issue and the child seems to rotate by the same amount when they are grouped together.
I've uploaded a demo video to try and explain:
http://www.youtube.com/watch?v=BzAKW4WBWYs
I've also pasted up the complete code for the components, the static pass through and the scene entity.
http://pastebin.com/5hEmiVx9
Thanks
Think wheels on a car. I want the right wheel to always be in the same
spot relative to the body of the car.
It sounds like you want to be able to locate the position of the wheel for any given orientation or position of the car. One built in method that XNA has to help here is Model.CopyAbsoluteBoneTransformsTo(Matrix[]); However, your code looks like you want to handle parent child relationship manually. So here is a way to do it without using the built in method. It assumes you do have offset information at load time:
Before the game loops starts (say, in the LoadContent method), after loading the car & wheel and assuming they load into the proper positions, you can then create your offset vector ( _parentOffset )
Vector3 _parentOffset = wheel.meshes[?].ParentBone.Transform.Translation - car.meshes[?].ParentBone.Transform.Translation;//where ? is the mesh index of the mesh you are setting up.
Save that vector and don't modify it.
Later, after the car's matrix has been rotationally and or positionally displaced, set the wheel's matrix like this:
Matrix wheelMatrix = carMatrix;
wheelMatrix.Translation += (wheelMatrix.Right * _parentOffset.X) +
(wheelMatrix.Up * _parentOffset.Y) +
(wheelMatrix.Backward * _parentOffset.Z);
This allows that the wheel matrix will inherit any rotational and translational information from the car but will displace the wheel's position appropriately regardless of car's orientation/position.
The distance between two objects is NOT a function of either orientations.
What you basically want is the distance of the child object to the orientation line of the parent object. Assuming you have a global cartesian coordinate system this can be simply calculated as h=sqrt(x^2+y^2)*sin(Theta), x and y being the relative coordinates of the child with respect to the parent and Theta the orientation of the parent measured from x axis.
But still the question is a little bit confusing to me. If you only want to make sure that the child is on the right side of the parent why don't you simply check the relative x? If it's positive it's on the right and if it's negative it's on the left?
The issue was the way I was trying to use the offset of the world space.
Thanks to flashed from #XNA on EFnet, this code works perfectly:
[Serializable]
public class Component_Child_fromxna : BaseComponentAutoSerialization<ISceneEntity>
{
Vector3 _parentOffset;
Matrix _ParentMatrixOffset;
public override void OnUpdate(GameTime gameTime)
{
// Get a sceneobject from the ParentObject
SceneObject sceneObject = (SceneObject)ParentObject;
// This relies on the position never being at 0,0,0 for setup, so please don't do that
// or change it with more look ups so that you don't need to rely on a Zero Vector3 :-)
if (PassThrough.GroupSetupMode || _parentOffset == Vector3.Zero)
{
if (PassThrough.ParentTranslation != Vector3.Zero)
{
// The old offset - This is just in world space though...
_parentOffset = sceneObject.World.Translation - PassThrough.ParentTranslation;
// Get the distance between the child and the parent which we keep as the offset
// Inversing the ParentMatrix and multiplying it by the childs matrix gives an offset
// The offset is stored as a relative xyz, based on the parents object space
_ParentMatrixOffset = sceneObject.World * Matrix.Invert(PassThrough.ParentMatrix);
}
}
else
{
if (_parentOffset != Vector3.Zero)
{
//Matrix pLocation = Matrix.CreateTranslation(_parentOffset);
//sceneObject.World = Matrix.Multiply(pLocation, PassThrough.ParentMatrix);
sceneObject.World = Matrix.Multiply(_ParentMatrixOffset, PassThrough.ParentMatrix);
}
}
}
}