Simple 3D AABB-Line Segment collision detection (intersection) - c#

I just need a method to tell me whether an axis aligned bounding box in 3D intersects a line segment (not a ray) or not. I do not need the points of intersection.
The box is defined by 2 opposite corners, and the line segment by its start and end points, something like this:
Boolean intersection(Vector3 boxStart, Vector3 boxEnd, Vector3 segmentStart, Vector3 segmentEnd){...}
I've done a lot of research, and havent been able to find a code (in C# or Java hopefully) that I can understand or at least use. I need the method and not a library that will do the job...
My problem is that it needs to be 100% precise, and if the segment just touches the box (i.e. they share a single point), it has to return false. For example, if the segment is one of the edges of the box or passes though a corner, they DO NOT intersect.
Thanks

In Java, either of the intersects() methods is a candidate; but due to implementation limitations, you'd need to test it with Line2D.

Related

Test if one GameObject is above another with any shape colliders

Essentially, I have a function designed to test if one object is positioned entirely above another while taking the collider bounds into account:
public static bool isAbove(GameObject a, GameObject b)
{
Collider2D colliderA = a.GetComponent<Collider2D>();
Collider2D colliderB = b.GetComponent<Collider2D>();
return a.transform.position.y - (colliderA.bounds.size.y * 0.5) >= b.transform.position.y + (colliderB.bounds.size.y * 0.5);
}
When I originally wrote this, I had no intention to use bounding shapes other than boxes, so the algorithm worked. Now, I am using a circle collider on one of the objects and a box collider on the other one, which makes the algorithm inconsistent, as it's still treating the circle as a box. I really want this working for any shape colliders in any combination.
I thought that I could specify a point directly below the first object and then find the max point at that x position, but I can't find this option anywhere, and I'm still not sure if it's the solution I should be looking for.
As I mentioned in my comment, Collision2D has a lot of useful information regarding the collision of two objects. Specifically for your use case, I would also look into the Vector3.Dot. To be brief, using Vector3(up, otherObject will give you a result to determine if two objects are over one another.
For a little more clarification, there are three possible cases that can be returned from Vector3.Dot and they are
Dot is 0 - The two objects are perfectly perpendicular to one another
Dot is <0 - The angle between the two objects is greater than 90º
Dot is >0 - The angle between the two objects is less than 90º
For your specific use case, I would calculate the dot product between the up vector, and the vector to the other target. If the result is greater than 0 then the other target is above your current object. You can either only check this data when the objects are actively colliding or check it every frame. It would depend on how many objects you're checking against.
This already exists anyway, you are looking for Collider2D.isTouching so you simply do
return colliderA.isTouching(colliderB);
and done ;)
However, instead of passing in GameObject and everytime use GetComponent you should rather somewhere pre-cache the Collider2D references and directly use either
if(colliderA.isTouching(colliderB))
or also
if(Physics2D.isTouching(colliderA, colliderB))
They are more or less equivalent.

How do I determine if i just calculated the normal in the correct direction?

To explain the context, I procedurally generate buildings on unity in C#. I create a mesh and fill in the vertices and triangles, then I calculate the normals of the different points. I have several hundreds of buildings that are generated, but some faces are not in the right direction, the normals point inwards instead of outwards.
The normals are good
The normals are bad
To calculate the normals I create a Plane with the different vertex that make up the triangle, and then I retrieve the normal of the Plane. I also tested the cross product that gives the same result.
Plane plane = new Plane(v1, v2, v3);
normals.Add(plane.normal);
How i generate Triangle ?
Ex: I make a for loop on the points at the base of the building.
vectors.Add(v1);
vectors.Add(v2);
vectors.Add(v3); //v3 = v1+height
vectors.Add(v4); //v4 = v2+height
// index values
int idx1, idx2, idx3, idx4;
idx4 = vectors.Count - 1;
idx3 = vectors.Count - 2;
idx2 = vectors.Count - 3;
idx1 = vectors.Count - 4;
// Triangle 1
indices.Add(idx1);
indices.Add(idx3);
indices.Add(idx2);
...
mesh.triangles = indices.ToArray();
So my question is: How to determine if the normal is in the right direction (inside or outside)? If I can determine that, I can then flip the normal and normally it will work.
I do not totally understand your question, but for simple shapes a simple algorithm is ..
just take the "center" of the object (the CG is fine) and make a vector from there to your vertex or triangle. That direction is "outside". If you're pointing over 90° away from that, you're pointing in to the guts of the object
the next more complicated approach ...
move along your normal say "one meter". call that point "test point". you should now be "outside" your building, correct?
now you just need to check if testPoint is inside or outside your 3D shape.
in short, to determine if you are inside or outside a 3D object, you just cast a ray and count how many times you intersect with the walls. if odd, you're inside, if even you're outside.
You can google hundreds of discussions on this on the www, example https://stackoverflow.com/a/63572837/294884
Note that there are many, many variations on this, and many problems too. In some cases you start from "just inside" your normal (ie go backwards a little); sometimes it's better to start from the middle of the object (if such a thing is knowable); sometimes there are issues about how the ray casting system works in edge cases (like "right on" the surface, which is what your vertex is)
the first solution seems to me to be the right one
It may be. Sometimes it is useless. It depends on the nature of your shapes.
I wanted to avoid having to do raycast ..
Can assure you - you will have to constantly raycast during any construction process! If you wish to "avoid" casting, set the idea aside. You will be casting until you are sick of it :)
I wanted to avoid having to do raycast to limit the generation time
The good news is this is totally incorrect. Casting is extremely trivial and a very minor burden compared to everything going on in a 3D scene. When you play any 3D scene, casts are being made 100s and 1000s of times each frame.
but if I have two buildings that are close to each other, the ray will find the wall but from the second building so I couldn't determine the normal is "inside" or "outside", right?
TBC in the simple system I described. You would certainly ONLY cast against that same building that you are working on! So that's the way to go.
But indeed, unrelated to what you're asking about. Say you're in a "city". You can indeed cast through "all walls" and the parity (ie: odd or even) will let you know if you are indoors or out. This has problems though, relating to edges, corners etc. But in some case it is relevant to that problem.
As mentioned on this answer https://stackoverflow.com/a/63593282/294884 ultimately you can investigate convex hulls and more. It's a big topic!
Note that often when you build dynamic buildings/shapes, you havce a data structure of each "wall" and indeed it knows which side is in and which side out. When you do that first, it's then easy to draw the triangles the correct way. It's a big topic!

Get Intersection line between two rectangles in 3D

I am trying to find a way to get the line (two points in 3D space) of the intersection between two rectangles.
I ran into this question: Intersection between two rectangles in 3D
But this is not my issue. In that question, the rectangle is treated as only the bounds (the perimeter), while I am looking for the rectangle as a whole (think about a picture frame vs the picture itself).
I've figured out that, in every case, there will either be an intersection line (two points), or no intersection at all. If the intersection was just on the borders, therefore just a point, it can be treated as no intersection in my case.
My scenario is that one of these rectangle represents a "static" surface, which cannot move or change. The other one represents a "dynamic" surface, which I have to adapt to avoid crossing
Example:
Once I obtain p1 and p2, which are points in the 3D space, my goal is to modify the Dynamic rectangle into a 3d polygon, which will no longer cross the static rectangle, like this:
So you can see why "edge intersections" are irrelevant to my situation. I am turning "real" intersections into edge intersections, so any edge intersection doesn't require me to do anything with it.
I am only looking for a formula, starting with two sets of 4 points (the rectangles), that would give me the two points of the line of their intersection, or would tell me that there is no (relevant) intersection.
Every formula I've found on this site or others doesn't fit my needs, or doesn't let me input arbitrary rectangles (for example, I can't fix my problem with a formula that uses planes or that treats a rectangle as simply 4 lines)
I am, of course, trying to code it (in C#), therefore any code answer is a great help, but I am confident that even a math-only answer would suffice for me to produce the code from it, therefore I will accept an answer that is only composed of pseudo-code or straight up mathematical formulas, provided they are either simple enough or explained well enough for me to understand what is happening.
If you are OK with just algorithm rather than full code here is a sketch:
Build 2 planes from the rectangles (any 3 points will do as in this answer)
Find the intersection line I of those 2 planes as in this answer or find out that the planes are parallel so there is no intersection
Find the intersections of the I line with the lines containing all sides of the rectangles as in this answer
Check whether some points found in the previous step lie inside the corresponding sides of the rectangles (line segments). This step potentially can be merged with the previous one, but I put it separately for simplicity. Now you potentially have 0, 1 or 2 segments that represent the intersections of the I line with your two rectangles (note that here point is treated as an edge case of a segment where both ends are the same). If you don't have 2 segments, there is no intersection of the rectangles.
Assuming at the previous step you found 2 segments (one in each rectangle) on the line I, you just need to find their intersection and it will be your answer (again, empty means no intersection).

Opinions on platform game actor/background collision resolving

Imagine the following scenario: I have a level whose physical structure is built up from a collection of bounding rectangles, combined with prerendered bitmap backgrounds. My actors, including the player character, all have their own bounding rectangle. If an actor manages to get stuck inside a level block, partially or otherwise, it'll need to be shifted out again, so that it is flush against the block.
The untested technique I thought up during bio break is as follows:
If an actor's box is found to intersect a level box, determine where the centerpoints of each rect are. If the actor's center is higher than the level box's, move the actor so that the bottom of the actor's rect is flush with the top of the level's rect, and vice versa if it's lower. Then do a similar thing horizontally.
Opinions on that? Suggestions on better methods?
Actually, the bounding rects are XNA BoundingBoxes with their Z spanning from -1 to 1, but it's still 2D gameplay.
Have you read the N Tutorials? They're a wonderful introduction, complete with little demos, of Separating Axis Theorem based collision detection and simple projection response. (They're actually used in the N game to great effect.) The tutorials cover more than you need, but they're very general (extensible to many other shapes), and start to touch on issues with fast-moving objects and other response techniques.
Even if you do decide to go with something simpler than a SAT implementation, this may give you a lot of good ideas.
(When you're done with that and if you want your mind blown, try looking into some of the presentations from the Game Developers Conference physics tutorial day, including realtimecollisiondetection.net publications, the essentialmath.com tutorial slides, both of those books, and/or other stuff linked from those sites. I'd highly recommend the GDC session itself, too. While we still don't need or particularly want fancy GJK on swept hulls on the handheld game platforms we work with, some of the simpler concepts such as "configuration spaces" and Minkowski sums and differences have greatly influenced how I think about physics and collision detection and how we implement it.)
What the "real" physics engines do is find the minimum penetration vector. That is - the smallest vector that represents how far inside each other the two objects penetrate.
For an AABB (axis-aligned bounding box) this is really easy to calculate.
(Consider making your own 2D AABB structure, it will be smaller and therefore better for performance.)
Once you have your minimum penetration vector, you can perform collision response. And the easiest response is to simply separate the two objects by that vector (or separate the one object if the other is static).
Here is a good reference, by the makers of N on how to do this for convex polygons and circles. You should be able to simplify this down for AABBs.
A lot depends on the details. A complete solution could take into account velocities or other issues. But treating this simply...
You don't want to always resolve vertically first. Imagine an actor nudges horizontally into a block. If you resolve vertically first then the actor will pop up above that block, when a small horizontal movement would have sufficed.
Find what the vertical and horizontal movements would need to be to "get out of collision", and then apply the one with the smallest absolute value.
Then repeat a few times, in case the movement puts the actor into another block. But don't repeat forever, because the actor could be wedged somewhere that never resolves.
Maybe if your last movement still leaves you in collision, you could just average the last two movements and leave it there.
Another possible approach is, rather than waiting for a collision and then shifting out, check for possible collisions before you move objects and, if there is going to be a collision, move the player only up to the edge of the block.
I.e., contrast how Adventure does collisions with walls: http://www.youtube.com/watch?v=I6-zN_eaRd8
to how most NES games do collisions with walls.

How To Make a Tetris Clone?

I am working on coding a Tetris clone in XNA C# and am unsure of the best way to approach the data structure side of the game on a high level.
I am totally fine with the collision detection, rotations, animation etc. What I need to know the best way to do the storing of "dropped blocks" - ie blocks that are no longer under tha player's control.
I think that each Tetromino block should be stored in its own class that consists of a 4x4 array so that the block can easily be rotated. The problem is then how to I store the tetromino's final position into the game grid by then cutting the tetromino up into individual blocks(for each cell) and then set the main game grid's corresponding positions to hold these same blocks, then disappearing the tetromino once it has reached its final position. Maybe there is some drawback to my method.
Should I create a 10x20 matrix for the main game grid which can then store? or should I use stacks or queues to somehow store the dropped blocks. Or maybe there is some better method/data structure to store things?
I am sure my way would work, but I am reaching out to see if anybody knows a better way or if my way is good enough?
P.S. Not homework, this will be a project for my portfolio. Thanks.
Once a block is immobile, there's nothing that distinguishes it from any other block that is now immobile. In that regard, I think it makes the most sense to store the entire grid as a matrix, where each square is either filled or not (along with the color of the block if it is).
I feel like the matrix has many advantages. It'll make collision detection simple (no having to compare with multiple objects, just locations on a matrix). Storing it as a matrix will also make it easier to determine when a full line has been created. On top of that, you don't have to worry about splicing an immobile Tetromino when a line disappears. And when one does, you can just shift the entire matrix down in one fell swoop.
This smells like homework, but my take on an object-oriented approach to Tetris would be to have each individual square be an object, and both "blocks" (tetrominos) and the grid itself would be collections of the same square objects.
Block objects manage the rotation and position of the falling squares, and the grid handles displaying them and detroying completed rows. Each block would have a colour or texture associated with it that would be provided by the original block object it came from, but otherwise squares at the base of the grid would have no other indication that they were ever part of the same original block.
To elaborate, when you create a new block object, it creates a set of 4 squares with the same colour/texture on the grid. The grid manages their display. So when the block hits the bottom, you just forget about the block, and the squares remain referenced by the grid.
Rotations and dropping are operations only a block need deal with, and only one its four squares (though it will need to be able to query the grid to make sure the rotation can fit).
Not making blocks actually look like autonomous blocks is - in my opinion - a big failing of many a Tetris clone. I put special effort into ensuring my clone always looked right, whether the block is still "in play" or dropped. This meant going slightly beyond the simple matrix data structure and coming up with something that supported the concept of "connection" between block parts.
I had a class called BlockGrid that is used as a base class for both a Block and the Board. BlockGrid has an abstract (pure virtual in C++) method called AreBlockPartsSameBlock that subclasses must override to determine whether two different block parts belong to the same block. For the implementation in Block, it simply returns true if there are block parts at both locations. For the implementation in Board, it returns true if both locations contain the same Block.
The BlockGrid class uses this information to "fill in" the details in the rendered blocks, so that they actually look like blocks.
Using arrays would be the easiest way to handle tetris. There is a direct correlation between what you see on screen and the structures used in memory. Using stack/queues would be an overkill and unnecessarily complicated.
You can have 2 copies of a falling block. One will be for display (Alpha) and the other one will be movement (Beta).
You will need a structure like
class FallingBlock
{
int pos_grid_x;
int pos_grid_y;
int blocks_alpha[4][4];
int blocks_beta[4][4];
function movedDown();
function rotate(int direction();
function checkCollision();
function revertToAlpha();
function copyToBeta()
};
The _beta array would be move or rotated and checked against the board for collisions. If there is a collision, revert it to _alpha, if not, copy _beta onto _alpha.
And if there is a collision on movedDown(), the block's life is over and the _alpha grid would have to copied onto the game board and the FallingBlock object deleted.
The board would of course have to be another structure like:
class Board
{
int gameBoard[10][20];
//some functions go here
}
I used int to represent a block, each value (like 1,2,3) representing a different texture or color (0 would mean an empty spot).
Once the block is part of the gameboard, it would only need a texture/color identifier to be displayed.
I actually just did this a few days ago except in WPF rather than XNA. Here's what I did:
Edit:
Seems like I define "Block" differently than other people. What I define as a Block is one of 4 cells that make up a Tetromino, and an actual Tetromino itself as a Piece.
Have a Block as a struct that had X, Y coordinates and Color. (I later added a bool IsSet to indicate whether it was in a floating piece or on the actual board, but that was just because I wanted to distinguish them visually)
As methods on Block, I had Left, Right, Down, and Rotate(Block center) which returned a new shifted Block. This allowed me to rotate or move any piece without knowing the shape or orientation of the piece.
I had a generic Piece object that had a List of all the blocks it contained and the index of the Block that was the center, which is used as the center of rotation.
I then made a PieceFactory that could produce all the different pieces, and with a Piece not needing to know what kind of piece it was, I could (and did) easily add variation of Pieces consisting of more or less than 4 Blocks without needing to create any new classes
The Board consisted of a Dictionary which was all the blocks that were currently on the board, as well as the dimensions of the board that was configurable. You can use a Matrix just as well probably, but with a Dictionary I only needed to iterate through Blocks without white spaces.
My Solution (design), with examples in Python as a good substitute for pseudo code.
Use a grid 20 x 10, that the tetrominoes fall down.
Tetrominoes are made up of blocks, which have attributes of coordinate (x,y) and colour.
So, for example, the T-shape tetrominoe looks like this...
. 4 5 6 7 8 .
.
19 # # #
20 #
.
Thus, the T-shape is a collection of blocks with the coords (5,19), (6,19), (7,19), (6,20).
Moving the shape is a matter of applying a simple transformation to all the coords in the group. e.g. to move the shape down add (0,1), left (-1,0) or right (1,0) to all coords in the collection that make the shape.
This also lets you use some simple trig to rotate the shape by 90-degrees. The rule is that when rotating 90-degrees relative to an origin, then (x,y) becomes equal to (-y,x).
Here is an example to explain it. Taking the T-shape from above, use the (6,19) as the centre block to rotate around. For simplicity, make this the first coordinate in the collection, so...
t_shape = [ [6,19], [5,19], [7,19], [6,20] ]
Then, here is a simple function to rotate that collection of coordinates by 90-degrees
def rotate( shape ):
X=0 # for selecting the X and Y coords
Y=1
# get the middle block
middle = shape[0]
# work out the coordinates of the other blocks relative to the
# middle block
rel = []
for coords in shape:
rel.append( [ coords[X]-middle[X], coords[Y]-middle[Y] ] )
# now rotate 90-degrees; x,y = -y, x
new_shape = []
for coords in rel:
new_shape.append( [ middle[X]-coords[Y], middle[Y]+coords[X] ] )
return new_shape
Now, if you apply this function to our collection of coordinate for the T-shape...
new_t_shape = rotate( t_shape )
new_t_shape
[[6, 19], [6, 18], [6, 20], [5, 19]]
Plot this out in the coordinate system and it looks like this...
. 4 5 6 7 8 .
.
18 #
19 # #
20 #
.
That was the hardest bit for me, hope this helps someone.
Keep in mind that a previous winner of the Obfuscated C Code Contest implemented a pretty good tetris game (for VT100 terminals on BSD unix) in fewer than 512 bytes of obfuscated C:
long h[4];t(){h[3]-=h[3]/3000;setitimer(0,h,0);}c,d,l,v[]={(int)t,0,2},w,s,I,K
=0,i=276,j,k,q[276],Q[276],*n=q,*m,x=17,f[]={7,-13,-12,1,8,-11,-12,-1,9,-1,1,
12,3,-13,-12,-1,12,-1,11,1,15,-1,13,1,18,-1,1,2,0,-12,-1,11,1,-12,1,13,10,-12,
1,12,11,-12,-1,1,2,-12,-1,12,13,-12,12,13,14,-11,-1,1,4,-13,-12,12,16,-11,-12,
12,17,-13,1,-1,5,-12,12,11,6,-12,12,24};u(){for(i=11;++i<264;)if((k=q[i])-Q[i]
){Q[i]=k;if(i-++I||i%12<1)printf("\033[%d;%dH",(I=i)/12,i%12*2+28);printf(
"\033[%dm "+(K-k?0:5),k);K=k;}Q[263]=c=getchar();}G(b){for(i=4;i--;)if(q[i?b+
n[i]:b])return 0;return 1;}g(b){for(i=4;i--;q[i?x+n[i]:x]=b);}main(C,V,a)char*
*V,*a;{h[3]=1000000/(l=C>1?atoi(V[1]):2);for(a=C>2?V[2]:"jkl pq";i;i--)*n++=i<
25||i%12<2?7:0;srand(getpid());system("stty cbreak -echo stop u");sigvec(14,v,
0);t();puts("\033[H\033[J");for(n=f+rand()%7*4;;g(7),u(),g(0)){if(c<0){if(G(x+
12))x+=12;else{g(7);++w;for(j=0;j<252;j=12*(j/12+1))for(;q[++j];)if(j%12==10){
for(;j%12;q[j--]=0);u();for(;--j;q[j+12]=q[j]);u();}n=f+rand()%7*4;G(x=17)||(c
=a[5]);}}if(c==*a)G(--x)||++x;if(c==a[1])n=f+4**(m=n),G(x)||(n=m);if(c==a[2])G
(++x)||--x;if(c==a[3])for(;G(x+12);++w)x+=12;if(c==a[4]||c==a[5]){s=sigblock(
8192);printf("\033[H\033[J\033[0m%d\n",w);if(c==a[5])break;for(j=264;j--;Q[j]=
0);while(getchar()-a[4]);puts("\033[H\033[J\033[7m");sigsetmask(s);}}d=popen(
"stty -cbreak echo stop \023;cat - HI|sort -rn|head -20>/tmp/$$;mv /tmp/$$ HI\
;cat HI","w");fprintf(d,"%4d on level %1d by %s\n",w,l,getlogin());pclose(d);}
http://www.ioccc.org/1989/tromp.hint
I'm by no means a Tetris expert, but as you described a 10x20 matrix seems like a natural choice to me.
It will make it very easy when the time comes to check if you have completed a line or not, and dealing with it. Simply iterating over the 2d-array looking at boolean values of each position to see if they add up to 10 block positions.
However, you'll have some manual clean up to do if there is a completed line. Having to shift everything down. All though it isn't that big of a deal when it comes down to it.
Using Simon Peverett logic, here is what I ended up with in c#
public class Tetromino
{
// Block is composed of a Point called Position and the color
public Block[] Blocks { get; protected internal set; }
// Constructors, etc.
// Rotate the tetromino by 90 degrees, clock-wise
public void Rotate()
{
Point middle = Blocks[0].Position;
List<Point> rel = new List<Point>();
foreach (Block b in Blocks)
rel.Add(new Point(b.Position.x - middle.x, b.Position.y - middle.y));
List<Block> shape = new List<Block>();
foreach (Point p in rel)
shape.Add(new Block(middle.x - p.y, middle.y + p.x));
Blocks = shape.ToArray();
}
public void Translate(Point p)
{
// Block Translation: Position+= p;
foreach (Block b in Blocks)
b.Translate(p);
}
}
Note: Using XNA, Point structure could be swapped for Vector2D
in my example (Java) - all figures have lists of blocks - which can be removed whenever needed. Also in my Board class I have a list of figures and a field variable figure - which is controlled by the user. When the figure is "landed" - it goes into the list of other figures, and a new figure is made controllable by the user.
A better explanation here: http://bordiani.wordpress.com/2014/10/20/tetris-in-java-part-i-overview/

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