#Polygon love 2 mods how to#

I'm not absolutely sure how to handle this case, I would not count it as intersection either way. What about COLLINEAR? It means both vectors lie on the same infinite line, depending on position and length, they don't intersect at all or they intersect in an endless number of points. YES increases intersections, NO does nothing. So you have 2 vectors, 4 points, 8 coordinates. The input values are the two endpoints of vector 1 ( v1x1/v1y1 and v1x2/v1y2) and vector 2 ( v2x1/v2y1 and v2x2/v2y2). If they are not collinear, they must intersect in exactly one point. means they intersect in any number of points from zero to infinite. vectors intersect in exactly one point or they are collinear, which If we get here, only two possibilities are left. However since vectors have a limited length, two vectors might not be parallel and still never intersect because they are too short to ever meet each other. Two lines in 2D space will always intersect exactly once, unless they are parallel, in which case they never intersect. The ray has to hit each side exactly once or never at all. Consider the ray to be a vector and every side to be a vector. You need to test the ray against all sides. Therefore we can't just work with the polygon points as before, now we need the actual sides. Now that we have the ray with its start and end coordinates, the problem shifts from ' is the point within the polygon' to ' how often does the ray intersects a polygon side'. If your pixel step width is 1.0, then just choose 1.0 (yet 0.1 would have worked as well) It depends on the coordinate system scale you use for drawing. How big should you choose e? Not too big. Since the bounding box might equal the polygon (if the polygon is an axis aligned rectangle, the bounding box is equal to the polygon itself!), we need some padding to make this safe, that's all. As I said, ray tracing fails if we start too close to a polygon line. the point (Xmin - e/p.y) is outside the polygon for sure.Д«ut what is e? Well, e (actually epsilon) gives the bounding box some padding. You still have the bounding box of above, remember? Just pick a point outside the bounding box and use it as starting point for your ray.

Ray casting may fail for points too close to a polygon side because of limited floating point precision and rounding issues, but in reality that is hardly a problem, as if a point lies that close to a side, it's often visually not even possible for a viewer to recognize if it is already inside or still outside. The winding number algorithm would be an alternative, it is more accurate for points being very close to a polygon line but it's also much slower. If the number of hits is even, it's outside of the polygon, if it's odd, it's inside. The idea of the algorithm is pretty simple: Draw a virtual ray from anywhere outside the polygon to your point and count how often it hits a side of the polygon. The easiest algorithm, that can handle all three cases above and is still pretty fast is named ray casting. Here are examples of solid ones (one convex, one concave): Which method works also depends on whether the polygon can have holes or will always be solid. There are a couple of ways how this can be calculated. To handle points that are within the bounding rectangle, we need a more sophisticated algorithm. As you can see, this test is ultra fast but it's also very coarse. This is the first test to run for any point. p is your point, p.x is the x coord, p.y is the y coord

A point outside of the rectangle with the two edges (2/1) and (9/7) cannot be within the polygon. This means Xmin is 2, Xmax is 9, Ymin is 1 and Ymax is 7. How does that work? Iterate over all points of the polygon and find the min/max values of X and Y.Д®.g. This is very easy, fast and can already save you a lot of calculations. Create an axis aligned bounding box around your polygon. Before you run any sophisticated algorithm, first do a simple test. Now you said speed is your main concern, okay, let's go for speed. After all, 3D APIs (OpenGL or Direct3D) also work with floats and modern graphics libraries very often take advantage of GPU acceleration.

Still, I never noticed that macOS UIs are significantly slower than other UIs. On retina screens half a point (0.5/0.5) is pixel. macOS only knows points and a point can translate to one pixel, but depending on monitor resolution, it might translate to something else. Many systems use integers for UI painting (pixels are ints after all), but macOS, for example, uses float for everything. For graphics, I'd rather not prefer integers.

Polygon love 2 mods