cocos2dx detect intersection with polygon sprite - c++

I am using cocos2d-x 3.8.
I try to create two polygon sprites with the following code.
I know we can detect intersect with BoundingBox but is too rough.
Also, I know we can use Cocos2d-x C++ Physics engine to detect collisions but doesn't it waste a lot of resource of the mobile device? The game I am developing does not need physics engine.
is there a way to detect the intersect of polygon sprites?
Thank you.
auto pinfoTree = AutoPolygon::generatePolygon("Tree.png");
auto treeSprite= Sprite::create(pinfoTree);
treeSprite-> setPosition(width / 4 * 3 - 30 , height / 2 - 200);
this->addChild(treeSprite);
auto pinfoBird = AutoPolygon::generatePolygon("Bird.png");
auto Bird= Sprite::create(pinfoTree);
Bird->setPosition(width / 4 * 3, height / 2);
this->addChild(Bird)

This is a bit more complicated: AutoPolygon gives you a bunch of triangles - the PhysicsBody::createPolygon requires a convex polygon with clockwise winding… so these are 2 different things. The vertex count might even be limited. I think Box2d’s maximum count for 1 polygon is 8.
If you want to try this you’ll have to merge the triangles to form polygons. An option would be to start with one triangle and add more as long as the whole thing stays convex. If you can’t add any more triangles start a new polygon. Add all the polygons as PhysicsShapes to your physics body to form a compound object.
I would propose that you don’t follow this path because
Autopolygon is optimized for rendering - not for best fitting
physics - that is a difference. A polygon traced with Autopolygon will always be bigger than the original sprite - Otherwise you would see rendering artifacts.
You have close to no control over the generated polygons
Tracing the shape in the app will increase your startup time
Triangle meshes and physics outlines are 2 different things
I would try some different approach: Generate the collision shapes offline. This gives you a bunch of advantages:
You can generate and tweak the polygons in a visual editor e.g. by
using PhysicsEditor
Loading the prepares polygons is way faster
You can set additional parameters like mass etc
The solution is battle proven and works out of the box
But if you want to know how polygon intersect work. You can look at this code.
// Calculate the projection of a polygon on an axis
// and returns it as a [min, max] interval
public void ProjectPolygon(Vector axis, Polygon polygon, ref float min, ref float max) {
// To project a point on an axis use the dot product
float dotProduct = axis.DotProduct(polygon.Points[0]);
min = dotProduct;
max = dotProduct;
for (int i = 0; i < polygon.Points.Count; i++) {
flaot d = polygon.Points[i].DotProduct(axis);
if (d < min) {
min = dotProduct;
} else {
if (dotProduct> max) {
max = dotProduct;
}
}
}
}
// Calculate the distance between [minA, maxA] and [minB, maxB]
// The distance will be negative if the intervals overlap
public float IntervalDistance(float minA, float maxA, float minB, float maxB) {
if (minA < minB) {
return minB - maxA;
} else {
return minA - maxB;
}
}
// Check if polygon A is going to collide with polygon B.
public boolean PolygonCollision(Polygon polygonA, Polygon polygonB) {
boolean result = true;
int edgeCountA = polygonA.Edges.Count;
int edgeCountB = polygonB.Edges.Count;
float minIntervalDistance = float.PositiveInfinity;
Vector edge;
// Loop through all the edges of both polygons
for (int edgeIndex = 0; edgeIndex < edgeCountA + edgeCountB; edgeIndex++) {
if (edgeIndex < edgeCountA) {
edge = polygonA.Edges[edgeIndex];
} else {
edge = polygonB.Edges[edgeIndex - edgeCountA];
}
// ===== Find if the polygons are currently intersecting =====
// Find the axis perpendicular to the current edge
Vector axis = new Vector(-edge.Y, edge.X);
axis.Normalize();
// Find the projection of the polygon on the current axis
float minA = 0; float minB = 0; float maxA = 0; float maxB = 0;
ProjectPolygon(axis, polygonA, ref minA, ref maxA);
ProjectPolygon(axis, polygonB, ref minB, ref maxB);
// Check if the polygon projections are currentlty intersecting
if (IntervalDistance(minA, maxA, minB, maxB) > 0)
result = false;
return result;
}
}
The function can be used this way
boolean result = PolygonCollision(polygonA, polygonB);

I once had to program a collision detection algorithm where a ball was to collide with a rotating polygon obstacle. In my case the obstacles where arcs with certain thickness. and where moving around an origin. Basically it was rotating in an orbit. The ball was also rotating around an orbit about the same origin. It can move between orbits. To check the collision I had to just check if the balls angle with respect to the origin was between the lower and upper bound angles of the arc obstacle and check if the ball and the obstacle where in the same orbit.
In other words I used the various constrains and properties of the objects involved in the collision to make it more efficient. So use properties of your objects to cause the collision. Try using a similar approach depending on your objects

Related

Frustum Culling Bug

So I've implemented Frustum Culling in my game engine and I'm experiencing a strange bug. I am rendering a building that is segmented into chunks and I'm only rendering the chunks which are in the frustum. My camera starts at around (-.033, 11.65, 2.2) and everything looks fine. I start moving around and there is no flickering. When I set a breakpoint in the frustum culling code I can see that it is indeed culling some of the meshes. Everything seems great. Then when I reach the center of the building, around (3.9, 4.17, 2.23) meshes start to disappear that are in view. The same is true on the other side as well. I can't figure out why this bug could exist.
I implement frustum culling by using the extraction method listed here Extracting View Frustum Planes (Gribb & Hartmann method). I had to use glm::inverse() rather than transpose as it suggested and I think the matrix math was given for row-major matrices so I flipped that. All in all my frustum plane calculation looks like
std::vector<Mesh*> render_meshes;
auto comboMatrix = proj * glm::inverse(view * model);
glm::vec4 p_planes[6];
p_planes[0] = comboMatrix[3] + comboMatrix[0]; //left
p_planes[1] = comboMatrix[3] - comboMatrix[0]; //right
p_planes[2] = comboMatrix[3] + comboMatrix[1]; //bottom
p_planes[3] = comboMatrix[3] - comboMatrix[1]; //top
p_planes[4] = comboMatrix[3] + comboMatrix[2]; //near
p_planes[5] = comboMatrix[3] - comboMatrix[2]; //far
for (int i = 0; i < 6; i++){
p_planes[i] = glm::normalize(p_planes[i]);
}
for (auto mesh : meshes) {
if (!frustum_cull(mesh, p_planes)) {
render_meshes.emplace_back(mesh);
}
}
I then decide to cull each mesh based on its bounding box (as calculated by ASSIMP with the aiProcess_GenBoundingBoxes flag) as follows (returning true means culled)
glm::vec3 vmin, vmax;
for (int i = 0; i < 6; i++) {
// X axis
if (p_planes[i].x > 0) {
vmin.x = m->getBBoxMin().x;
vmax.x = m->getBBoxMax().x;
}
else {
vmin.x = m->getBBoxMax().x;
vmax.x = m->getBBoxMin().x;
}
// Y axis
if (p_planes[i].y > 0) {
vmin.y = m->getBBoxMin().y;
vmax.y = m->getBBoxMax().y;
}
else {
vmin.y = m->getBBoxMax().y;
vmax.y = m->getBBoxMin().y;
}
// Z axis
if (p_planes[i].z > 0) {
vmin.z = m->getBBoxMin().z;
vmax.z = m->getBBoxMax().z;
}
else {
vmin.z = m->getBBoxMax().z;
vmax.z = m->getBBoxMin().z;
}
if (glm::dot(glm::vec3(p_planes[i]), vmin) + p_planes[i][3] > 0)
return true;
}
return false;
Any guidance?
Update 1: Normalizing the full vec4 representing the plane is incorrect as only the vec3 represents the normal of the plane. Further, normalization is not necessary for this instance as we only care about the sign of the distance (not the magnitude).
It is also important to note that I should be using the rows of the matrix not the columns. I am achieving this by replacing
p_planes[0] = comboMatrix[3] + comboMatrix[0];
with
p_planes[0] = glm::row(comboMatrix, 3) + glm::row(comboMatrix, 0);
in all instances.
You are using GLM incorrectly. As per the paper of Gribb and Hartmann, you can extract the plane equations as a sum or difference of different rows of the matrix, but in glm, mat4 foo; foo[n] will yield the n-th column (similiar to how GLSL is designed).
This here
for (int i = 0; i < 6; i++){
p_planes[i] = glm::normalize(p_planes[i]);
}
also doesn't make sense, since glm::normalize(vec4) will simply normalize a 4D vector. This will result in the plane to be shifted around along its normal direction. Only thexyz components must be brought to unit length, and w must be scaled accordingly. It is even explained in details in the paper itself. However, since you only need to know on which half-space a point lies, normalizing the plane equation is a waste of cycles, you only care about the sign, not the maginitude of the value anyway.
After following #derhass solution for normalizing the planes correctly for intersection tests you would do as follows
For bounding box plane intersection after projecting your box onto that plane which we call p and after calculating the midpoint of the box say m and after calculating the distance of that mid point from the plane say d to check for intersection we do
d<=p
But for frustum culling we just don't want our box to NOT intersect wih our frustum plane but we want it to be at -p distance from our plane and only then we know for sure that NO PART of our box is intersecting our plane that is
if(d<=-p)//then our box is fully not intersecting our plane so we don't draw it or cull it[d will be negative if the midpoint lies on the other side of our plane]
Similarly for triangles we have check if the distance of ALL 3 points of the triangle from the plane are negative.
To project a box onto a plane we take the 3 axises[x,y,z UNIT VECTORS] of the box,scale them by the boxes respective HALF width,height,depth and find the sum of each of their dot products[Take only the positive magnitude of each dot product NO SIGNED DISTANCE] with the planes normal which will be your 'p'
Not with the above approach for an AABB you can also cull against OOBB's with the same approach cause only the axises will change.
EDIT:
how to project a bounding box onto a plane?
Let's consider an AABB for our example
It has the following parameters
Lower extent Min(x,y,z)
Upper extent Max(x,y,z)
Up Vector U=(0,1,0)
Left Vector. L=(1,0,0)
Front Vector. F=(0,0,1)
Step 1: calculate half dimensions
half_width=(Max.x-Min.x)/2;
half_height=(Max.y-Min.y)/2;
half_depth=(Max.z-Min.z)/2;
Step 2: Project each individual axis of the box onto the plane normal,take only the positive magnitude of each dot product scaled by each half dimension and find the total sum. make sure both the box axis and the plane normal are unit vectors.
float p=(abs(dot(L,N))*half_width)+
(abs(dot(U,N))*half_height)+
(abs(dot(F,N))*half_depth);
abs() returns absolute magnitude we want it to be positive
because we are dealing with distances
Where N is the planes normal unit vector
Step 3: compute mid point of box
M=(Min+Max)/2;
Step 4: compute distance of the mid point from plane
d=dot(M,N)+plane.w
Step 5: do the check
d<=-p //return true i.e don't render or do culling
U can see how to use his for OOBB where the U,F,L vectors are the axises of the OOBB and the centre(mid point) and half dimensions are parameters you pass in manually
For an sphere as well you would calculate the distance of the spheres center from the plane (called d) but do the check
d<=-r //radius of the sphere
Put this in an function called outside(Plane,Bounds) which returns true if the bounds is fully outside the plane then for each of the 6 planes
bool is_inside_frustum()
{
for(Plane plane:frustum_planes)
{
if(outside(plane,AABB))
{
return false
}
}
return true;
}

Space carving of tetrahedra [duplicate]

I have the following problem as shown in the figure. I have point cloud and a mesh generated by a tetrahedral algorithm. How would I carve the mesh using the that algorithm ? Are landmarks are the point cloud ?
Pseudo code of the algorithm:
for every 3D feature point
convert it 2D projected coordinates
for every 2D feature point
cast a ray toward the polygons of the mesh
get intersection point
if zintersection < z of 3D feature point
for ( every triangle vertices )
cull that triangle.
Here is a follow up implementation of the algorithm mentioned by the Guru Spektre :)
Update code for the algorithm:
int i;
for (i = 0; i < out.numberofpoints; i++)
{
Ogre::Vector3 ray_pos = pos; // camera position);
Ogre::Vector3 ray_dir = (Ogre::Vector3 (out.pointlist[(i*3)], out.pointlist[(3*i)+1], out.pointlist[(3*i)+2]) - pos).normalisedCopy(); // vertex - camea pos ;
Ogre::Ray ray;
ray.setOrigin(Ogre::Vector3( ray_pos.x, ray_pos.y, ray_pos.z));
ray.setDirection(Ogre::Vector3(ray_dir.x, ray_dir.y, ray_dir.z));
Ogre::Vector3 result;
unsigned int u1;
unsigned int u2;
unsigned int u3;
bool rayCastResult = RaycastFromPoint(ray.getOrigin(), ray.getDirection(), result, u1, u2, u3);
if ( rayCastResult )
{
Ogre::Vector3 targetVertex(out.pointlist[(i*3)], out.pointlist[(3*i)+1], out.pointlist[(3*i)+2]);
float distanceTargetFocus = targetVertex.squaredDistance(pos);
float distanceIntersectionFocus = result.squaredDistance(pos);
if(abs(distanceTargetFocus) >= abs(distanceIntersectionFocus))
{
if ( u1 != -1 && u2 != -1 && u3 != -1)
{
std::cout << "Remove index "<< "u1 ==> " <<u1 << "u2 ==>"<<u2<<"u3 ==> "<<u3<< std::endl;
updatedIndices.erase(updatedIndices.begin()+ u1);
updatedIndices.erase(updatedIndices.begin()+ u2);
updatedIndices.erase(updatedIndices.begin()+ u3);
}
}
}
}
if ( updatedIndices.size() <= out.numberoftrifaces)
{
std::cout << "current face list===> "<< out.numberoftrifaces << std::endl;
std::cout << "deleted face list===> "<< updatedIndices.size() << std::endl;
manual->begin("Pointcloud", Ogre::RenderOperation::OT_TRIANGLE_LIST);
for (int n = 0; n < out.numberofpoints; n++)
{
Ogre::Vector3 vertexTransformed = Ogre::Vector3( out.pointlist[3*n+0], out.pointlist[3*n+1], out.pointlist[3*n+2]) - mReferencePoint;
vertexTransformed *=1000.0 ;
vertexTransformed = mDeltaYaw * vertexTransformed;
manual->position(vertexTransformed);
}
for (int n = 0 ; n < updatedIndices.size(); n++)
{
int n0 = updatedIndices[n+0];
int n1 = updatedIndices[n+1];
int n2 = updatedIndices[n+2];
if ( n0 < 0 || n1 <0 || n2 <0 )
{
std::cout<<"negative indices"<<std::endl;
break;
}
manual->triangle(n0, n1, n2);
}
manual->end();
Follow up with the algorithm:
I have now two versions one is the triangulated one and the other is the carved version.
It's not not a surface mesh.
Here are the two files
http://www.mediafire.com/file/cczw49ja257mnzr/ahmed_non_triangulated.obj
http://www.mediafire.com/file/cczw49ja257mnzr/ahmed_triangulated.obj
I see it like this:
So you got image from camera with known matrix and FOV and focal length.
From that you know where exactly the focal point is and where the image is proected onto the camera chip (Z_near plane). So any vertex, its corresponding pixel and focal point lies on the same line.
So for each view cas ray from focal point to each visible vertex of the pointcloud. and test if any face of the mesh hits before hitting face containing target vertex. If yes remove it as it would block the visibility.
Landmark in this context is just feature point corresponding to vertex from pointcloud. It can be anything detectable (change of intensity, color, pattern whatever) usually SIFT/SURF is used for this. You should have them located already as that is the input for pointcloud generation. If not you can peek pixel corresponding to each vertex and test for background color.
Not sure how you want to do this without the input images. For that you need to decide which vertex is visible from which side/view. May be it is doable form nearby vertexes somehow (like using vertex density points or corespondence to planar face...) or the algo is changed somehow for finding unused vertexes inside mesh.
To cast a ray do this:
ray_pos=tm_eye*vec4(imgx/aspect,imgy,0.0,1.0);
ray_dir=ray_pos-tm_eye*vec4(0.0,0.0,-focal_length,1.0);
where tm_eye is camera direct transform matrix, imgx,imgy is the 2D pixel position in image normalized to <-1,+1> where (0,0) is the middle of image. The focal_length determines the FOV of camera and aspect ratio is ratio of image resolution image_ys/image_xs
Ray triangle intersection equation can be found here:
Reflection and refraction impossible without recursive ray tracing?
If I extract it:
vec3 v0,v1,v2; // input triangle vertexes
vec3 e1,e2,n,p,q,r;
float t,u,v,det,idet;
//compute ray triangle intersection
e1=v1-v0;
e2=v2-v0;
// Calculate planes normal vector
p=cross(ray[i0].dir,e2);
det=dot(e1,p);
// Ray is parallel to plane
if (abs(det)<1e-8) no intersection;
idet=1.0/det;
r=ray[i0].pos-v0;
u=dot(r,p)*idet;
if ((u<0.0)||(u>1.0)) no intersection;
q=cross(r,e1);
v=dot(ray[i0].dir,q)*idet;
if ((v<0.0)||(u+v>1.0)) no intersection;
t=dot(e2,q)*idet;
if ((t>_zero)&&((t<=tt)) // tt is distance to target vertex
{
// intersection
}
Follow ups:
To move between normalized image (imgx,imgy) and raw image (rawx,rawy) coordinates for image of size (imgxs,imgys) where (0,0) is top left corner and (imgxs-1,imgys-1) is bottom right corner you need:
imgx = (2.0*rawx / (imgxs-1)) - 1.0
imgy = 1.0 - (2.0*rawy / (imgys-1))
rawx = (imgx + 1.0)*(imgxs-1)/2.0
rawy = (1.0 - imgy)*(imgys-1)/2.0
[progress update 1]
I finally got to the point I can compile sample test input data for this to get even started (as you are unable to share valid data at all):
I created small app with hard-coded table mesh (gray) and pointcloud (aqua) and simple camera control. Where I can save any number of views (screenshot + camera direct matrix). When loaded back it aligns with the mesh itself (yellow ray goes through aqua dot in image and goes through the table mesh too). The blue lines are casted from camera focal point to its corners. This will emulate the input you got. The second part of the app will use only these images and matrices with the point cloud (no mesh surface anymore) tetragonize it (already finished) now just cast ray through each landmark in each view (aqua dot) and remove all tetragonals before target vertex in pointcloud is hit (this stuff is not even started yet may be in weekend)... And lastly store only surface triangles (easy just use all triangles which are used just once also already finished except the save part but to write wavefront obj from it is easy ...).
[Progress update 2]
I added landmark detection and matching with the point cloud
as you can see only valid rays are cast (those that are visible on image) so some points on point cloud does not cast rays (singular aqua dots)). So now just the ray/triangle intersection and tetrahedron removal from list is what is missing...

3D Collision resolution, moving AABB + polyhedron

I have been writing a game engine in my free time, but I've been stuck for a couple weeks trying to get collisions working.
Currently I am representing entities' colliders with AABBs, and the collider for a level is represented by a fairly simple (but not necessarily convex) polyhedron. All the drawing is sprite-based but the underlying collision code is 3D.
I've got AABB/triangle collision detection working using this algorithm, (which I can naively apply to every face in the level mesh), but I am stuck trying to resolve the collision after I have detected its existence.
The algorithm I came up with works pretty well, but there are some edge cases where it breaks. For example, walking straight into a sharp corner will always push the player to one side or the other. Or if a small colliding face happens to have a normal that is closer to the players direction of movement than all other faces, it will "pop" the player in that direction first, even though using the offset from a different face would have had a better result.
For reference, my current algorithm looks like:
Create list of all colliding faces
Sort list in increasing order of the angle between face normal and negative direction of entity movement (i.e. process faces with the most "stopping power" first)
For each colliding face in collision list:
scale = distance of collision along face normal
Entity position += face normal * scale
If no more collision:
break
And here's the implementation:
void Mesh::handleCollisions(Player& player) const
{
using Face = Face<int32_t>;
BoundingBox<float> playerBounds = player.getGlobalBounds();
Vector3f negPlayerDelta = -player.getDeltaPos(); // Negative because face norm should be opposite direction of player dir
auto comparator = [&negPlayerDelta](const Face& face1, const Face& face2) {
const Vector3f norm1 = face1.normal();
const Vector3f norm2 = face2.normal();
float closeness1 = negPlayerDelta.dot(norm1) / (negPlayerDelta.magnitude() * norm1.magnitude());
float closeness2 = negPlayerDelta.dot(norm2) / (negPlayerDelta.magnitude() * norm2.magnitude());
return closeness1 > closeness2;
};
std::vector<Face> collidingFaces;
for (const Face& face : _faces)
{
::Face<float> floatFace(face);
if (CollisionHelper::collisionBetween(playerBounds, floatFace))
{
collidingFaces.push_back(face);
}
}
if (collidingFaces.empty()) {
return;
}
// Process in order of "closeness" between player delta and face normal
std::sort(collidingFaces.begin(), collidingFaces.end(), comparator);
Vector3f totalOffset;
for (const Face& face : collidingFaces)
{
const Vector3f& norm = face.normal().normalized();
Point3<float> closestVert(playerBounds.xMin, playerBounds.yMin, playerBounds.zMin); // Point on AABB that is most negative in direction of norm
if (norm.x < 0)
{
closestVert.x = playerBounds.xMax;
}
if (norm.y < 0)
{
closestVert.y = playerBounds.yMax;
}
if (norm.z < 0)
{
closestVert.z = playerBounds.zMax;
}
float collisionDist = closestVert.vectorTo(face[0]).dot(norm); // Distance from closest vert to face
Vector3f offset = norm * collisionDist;
BoundingBox<float> newBounds(playerBounds + offset);
totalOffset += offset;
if (std::none_of(collidingFaces.begin(), collidingFaces.end(),
[&newBounds](const Face& face) {
::Face<float> floatFace(face);
return CollisionHelper::collisionBetween(newBounds, floatFace);
}))
{
// No more collision; we are done
break;
}
}
player.move(totalOffset);
Vector3f playerDelta = player.getDeltaPos();
player.setVelocity(player.getDeltaPos());
}
I have been messing with sorting the colliding faces by "collision distance in the direction of player movement", but I haven't yet figured out an efficient way to find that distance value for all faces.
Does anybody know of an algorithm that would work better for what I am trying to accomplish?
I'm quite suspicious with the first part of code. You modify the entity's position in each iteration, am I right? That might be able to explain the weird edge cases.
In a 2D example, if a square walks towards a sharp corner and collides with both walls, its position will be modified by one wall first, which makes it penetrate more into the second wall. And then the second wall changes its position using a larger scale value, so that it seems the square is pushed only by one wall.
If a collision happens where the surface S's normal is close to the player's movement, it will be handled later than all other collisions. Note that when dealing with other collisions, the player's position is modified, and likely to penetrate more into surface S. So at last the program deal with collision with surface S, which pops the player a lot.
I think there's a simple fix. Just compute the penetrations at once, and use a temporal variable to sum up all the displacement and then change the position with the total displacement.

How do I calculate collision with rotation in 3D space?

In my program I need to calculate collision between a rotated box and a sphere as well as collision between 2 rotated boxes. I can't seem to find any information on it and trying to figure the math out in my own is boggling my mind.
I have collision working for 2 boxes and a sphere and a box, but now I need to factor in angles. This is my code so far:
class Box
{
public:
Box();
private:
float m_CenterX, m_CenterY, m_CenterZ, m_Width, m_Height, m_Depth;
float m_XRotation, m_YRotation, m_ZRotation;
};
class Sphere
{
public:
Sphere();
private:
float m_CenterX, m_CenterY, m_CenterZ, radius;
unsigned char m_Colour[3];
};
bool BoxBoxCollision(BoxA, BoxB)
{
//The sides of the Cubes
float leftA, leftB;
float rightA, rightB;
float topA, topB;
float bottomA, bottomB;
float nearA, nearB;
float farA, farB;
//center pivot is at the center of the object
leftA = A.GetCenterX() - A.GetWidth();
rightA = A.GetCenterX() + A.GetWidth();
topA = A.GetCenterY() - A.GetHeight();
bottomA = A.GetCenterY() + A.GetHeight();
farA = A.GetCenterZ() - A.GetDepth();
nearA = A.GetCenterZ() + A.GetDepth();
leftB = B.GetCenterX() - B.GetWidth();
rightB = B.GetCenterX() + B.GetWidth();
topB = B.GetCenterY() - B.GetHeight();
bottomB = B.GetCenterY() + B.GetHeight();
farB = B.GetCenterZ() - B.GetDepth();
nearB = B.GetCenterZ() + B.GetDepth();
//If any of the sides from A are outside of B
if( bottomA <= topB ) { return false; }
if( topA >= bottomB ) { return false; }
if( rightA <= leftB ) { return false; }
if( leftA >= rightB ) { return false; }
if( nearA <= farB ) { return false; }
if( farA >= nearB ) { return false; }
//If none of the sides from A are outside B
return true;
}
bool SphereBoxCollision( Sphere& sphere, Box& box)
{
float sphereXDistance = abs(sphere.getCenterX() - box.GetCenterX());
float sphereYDistance = abs(sphere.getCenterY() - box.GetCenterY());
float sphereZDistance = abs(sphere.getCenterZ() - box.GetCenterZ());
if (sphereXDistance >= (box.GetWidth() + sphere.getRadius())) { return false; }
if (sphereYDistance >= (box.GetHeight() + sphere.getRadius())) { return false; }
if (sphereZDistance >= (box.GetDepth() + sphere.getRadius())) { return false; }
if (sphereXDistance < (box.GetWidth())) { return true; }
if (sphereYDistance < (box.GetHeight())) { return true; }
if (sphereZDistance < (box.GetDepth())) { return true; }
float cornerDistance_sq = ((sphereXDistance - box.GetWidth()) * (sphereXDistance - box.GetWidth())) +
((sphereYDistance - box.GetHeight()) * (sphereYDistance - box.GetHeight()) +
((sphereYDistance - box.GetDepth()) * (sphereYDistance - box.GetDepth())));
return (cornerDistance_sq < (sphere.getRadius()*sphere.getRadius()));
}
How do I factor in rotation? Any suggestions would be great.
First of all, your objects are boxes, not rectangles. The term rectangle is strictly reserved for the 2D figure.
When you are dealing with rotations, you should generally view them as a special form of an affine transform. An affine transform can be a rotation, a translation, a scaling operation, a shearing operation, or any combination of these, and it can be represented by a simple 4x4 matrix that is multiplied to the vectors that give the vertices of your boxes. That is, you can describe any rotated, scaled, sheared box as the unit box (the box between the vectors <0,0,0> to <1,1,1>) to which an affine transform has been applied.
The matrix of most affine transforms (except those that scale by a factor of zero) can be inverted, so that you can both transform any point into the coordinate system of the box and then compare it against <0,0,0> and <1,1,1> to check whether its inside the box, and transform any point in the coordinates of the box back into your world coordinate system (for instance you can find the center of your box by transforming the vector <0.5, 0.5, 0.5>). Since any straight line remains a straight line when an affine transform is applied to it, all you ever need to transform is the vertices of your boxes.
Now, you can just take the vertices of one box (<0,0,0>, <0,0,1>, ...), transform them into your world coordinate system, then transform them back into the coordinate system of another box. After that, the question whether the two boxes overlap becomes the question whether the box described by the transformed eight vertices overlaps the unit box. Now you can easily decide whether there is a vertex above the base plane of the unit box (y > 0), below the top plane (y < 1), and so on. Unfortunately there is a lot of cases to cover for a box/box intersection, it is much easier to intersect spheres, rays, planes, etc. than such complex objects like boxes. However, having one box nailed to the unit box should help a lot.
Sidenote:
For rotations in 3D, it pays to know how to use quaternions for that. Euler angles and similar systems all have the issue of gimbal lock, quaternions do not have this restriction.
Basically, every unit quaternion describes a rotation around a single, free axis. When you multiply two unit quaternions, you get a third one that gives you the rotation that results from applying the two quaternions one after the other. And, since it is trivial to compute the multiplicative inverse of a quaternion, you can also divide one quaternion by another to answer the question what one-axis rotation you would need to apply to get from one rotation state to another. That last part is simply impossible to do in terms of Euler angles. Quaternions are really one of the sweetest parts of mathematics.
I simply cannot cover all the details in this answer, the topic is quite a broad and interesting one. That is why I linked the four wikipedia articles. Read them if you need further details.
For Box-Box collision transform the coordinates in such a way that the first box is centered at the origin and is aligned with the axis. Then checking if the second box collides with it is easier even tho is not quite trivial. For most cases (physics engine at small dt*v where you can assume movement is continuous) it suffices to check if any of the vertices fall inside the first box.
For Box-Sphere is simpler. Like before, transform the coordinates in such a way that the box is centered at the origin and is aligned with the axis. Now you only need to check that the distance between the center of the box and each of the canonical planes (generated by the axes) is less than the radius of the sphere plus half of the span of the box in the normal direction.

OpenGL-How do I draw randomly non-overlapping circle

I've already draw few random placed circle, but I want different numbers of circles every time I run the program. So the question really is how do I call a function in random times?
I also need them to have convex and concave effects but unable to arrange them to random circles.
Finally, I need circles not to overlap, how do I do that?
Below is my partial code so far.
void circle(){
double r=50;
int dx, dy;
dx=rand()%350;
dy=rand()%250;
glLineWidth(1);
glEnable(GL_LINE_SMOOTH);
glBegin(GL_LINES);
double i=1.0;
double j=0.0;
for (double y=r; y>=-r; y=y-1) {
i=i-0.01;
j=j+0.01;
//glColor3f(i, i, i);
glColor3f(j, j, j);
glVertex2f(-sqrt(r*r-y*y)+dx, y+dy);
glVertex2f(sqrt(r*r-y*y)+dx, y+dy);
}
glEnd();
}
void display(void){
glClear(GL_COLOR_BUFFER_BIT);
srand((unsigned)time(0));
circle();
circle();
circle();
glEnd();
glFlush();
}
The simple approach
It is enough to pick a random number and iterate. This can cause the circles to overlap.
int min_circles = 10;
int max_circles = 100;
int amount = min_circles + rand()%(max_circles-min_circles+1);
for (int i = 0; i < amount; i++)
circle();
Non overlapping
This is not a trivial matter and has been an interesting research topic. You can have several approaches to this problem for example:
Naïve Generation
Store all previously added circle positions and if you try to add a new one just do a check with the previous for overlapping. If it overlaps choose another position. If it fails several times in a row then stop.
Easing
You can also consider treating all circles as a system of points connected with springs and iterate a few times so that the springs will repel the circles from each other thus conforming to the non-overlapping rule.
Poisson Disk Sampling
You can read up on implementing Poisson Disk Sampling on the internet. The algorithm generates a uniform random distribution of points on a plane so that they are at certain distance from each other. Then just use these points as centers of circles.
how do I call a function in random times?
that one way of doing it:
if (rand() % someNumber == 0)
callFunc();
I also need them to have convex and concave effects but unable to arrange them to random circles.
i didnt understand what you mean.
Finally, I need circles not to overlap, how do I do that?
first you need to creaye circles in a structure, and store them in a collection. assume you the structure like that:
struct Circle {
float x, y, raduis;
}
and a collection like that:
std::vector<Circle> circles;
then the creation may look like that:
Circle c;
do {
bool canExit = true;
c.x = rand()*350;
c.y = rand()*250;
c.radius = 50;
for (int i = 0; i < circles.size(); i++) {
float dx = (circles[i].x - c.x);
float dy = (circles[i].y - c.y);
floar radii = circles[i].radius + c.radius;
if (dx*dx + dy*dy < (radii*radii) ) {
canExit = false;
break;
}
}
while(canExit == false);
circles.push_back(c);
of cours thats only may way, hope it works for you, and good luck.