I want to detect if ellipse collides with another ellipse and rectangle. How I can do it?
I'm writing in C++. I want to use it for a game.
If this is for a game, then exactness should not be an issue.
Treat your ellipse as a polygon, that is, choose N evenly distributed points on your ellipse and treat is as a polygon. Adjuct N to the level of the desired correctness.
Now you need to test if a convex polygon collides with a rectangle. And the latter is a convex polygon as well. Here's a link for convex polygon collision detection
If you need precise answer, than you have to describe your figures as functions and use Newton's method for finding intersection points
Related
In my current c++ program I am dealing with a plane that is intersected by several other planes. I want to find the polygon formed by the lines that define the intersections of the planes. For simplicity and computation speed, it seems like my best bet is to get the lines that form the intersections and then work out the polygon in 2d on the surface of the plane. Does anyone have an idea how to translate the lines(represented by a position and a direction vector) onto the plane and the final polygon back into 3d?
In general, this isn't possible to do. The simplest counterexample is the intersection of two planes where the two centers overlap. Viewing it edge-on, it would look like a plus sign. There is no polygon that results from this intersection; a line segment, yes, but no polygon. If you want to draw the resulting polygon, then it needs to be convex, as well which puts more constraints on the allowable intersection configurations.
I have a lunar lander type game. I don't use any physics engines.
My lander keeps falling if you do not use thruster and eventually lands on the ground. Ground is hand drawn, it is not a line, more like curve, and the land can be of any configuration or color.
How do I properly use collision detection and its results?
Well it depends on what you want to do. I would recommend one of the following:
Use physics engines. They are there for something. You could create different shapes what was drawn. You could mix in a rectangle if theres a straight line, or a lot of circles for curves, etc.
Use your own custom circle collision detector. You represent the lander with a bounding box sized circle. Then, for each of the handdrawn lines, create a bunch of adjacent circles representing the line. When you check your lander position, you are just basically looping through the circles representing the lines and checking for collisions. Incoming pseudocode
for (CollisionCircle* circle in collisions)
{
if (circle.collidesWith(lander.collisionCircle))
{
// 1. Calculate edge distance from lander to circle (position + radius distance)
// 2. Remove distance from lander position to fix position.
}
}
Here is another geometric problem:
I have created an 3-dimensional triangulated iso-surface of a point cloud using the marching cubes algorithm. Then I intersect this iso-surface with a plane and get a number of line segments that represent the contour lines of the intersection.
Is there any possibility to sort the vertices of these line segments clockwise so that I can draw them as a closed path and do a flood fill?
Thanks in advance!
It depends on how complex your isosurface is, but the simplest thing I can think of that might work is:
For each point, project to the plane. This will give you a set of points in 2d.
Make sure these are centered, via a translation to the centroid or center of the bounding box.
For each 2d point, run atan2 and get an angle. atan2 just puts things in the correct quadrant.
Order by that angle
If your isosurface/plane is monotonically increasing in angle around the centroid, then this will work fine. If not, then you might need to find the 2 nearest neighbors to each point in the plane, and hope that that makes a simple loop. In face, the simple loop idea might be simpler, because you don't need to project and you don't need to compute angles - just do everything in 3d.
This polygon could be shaped like a C
I tried the formula located here
How can I determine whether a 2D Point is within a Polygon?
however it doesn't actually correctly predict if the point is in the polygon.
Easiest way - especially for lots of points is to triangulate the polygon then do a point in triangle test.
You could convert the polygon into a set of convex polygons but that is trickier.
See also Random points inside a 4-sided Polygon
I have a need to calculate the minimum area rectangle (smallest possible rectangle) around the polygon.
The only input i have is the number of points in polygon.
I have the co-ordinates of the points also.
This is called Minimum Bounding Box, it's most basic algorithm used in OCR packages. You can find an implementation using Rotating Calipers from the OpenCV package. Once you get the source code, check out this file,
cv/src/cvrotcalipers.cpp
The method you need is cvMinAreaRect2().
Use the rotating calipers algorithm for a convex polygon, or the convex hull otherwise. You will of course need the coordinates of the points in the polygon, not just the number of points.
First do a grahm-scan and get the convex hull of the set of points. Then you can use something like minimum rectangle discussed here
Follow the following algorithm
Rotate the polygon onto the XY plane
Pick 1 edge and align this edge with the X axis(use arctan). Use the min/max x,y to find the bounding rectangle. Compute Area and store in list
Do the same for remaining edges in clipped polygon.
Pick the rectangle with the minimum Area.
Rotate Bounding Rectangle back for Coplanar reverse rotation of Step 1 and step 2
for more detail check link Minimum-Area-Rectangle
Obviously, you'll need the coordinates of the points to get the answer. If the rectangle is aligned to the X and Y aces, then the solution is trivial. If you want the smallest possible rectangle, at any angle, then you'll need to do some sort of optimization process.