A branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.

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5
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5answers
5k views

How can I test whether points are within a polygon?

I have 2D-points, which boundaries depict a polygon. The points are at integer positions (no fractions possible). Now I want to build an enumerator in C# that returns all points that are inside the ...
33
votes
6answers
3k views

Hexagon collision detection for fast moving objects?

A object has a position and a speed vector. Usually only the position is used to check if two objects collide, this is problematic for very fast moving objects as it can happen that the object moves ...
3
votes
3answers
2k views

How do I interpret the dot product of non-normalized vectors?

I know that if you take the dot-product of two normalized vectors, you get the cosine of the angle between them. But if I take the dot-product of two non-normalized vectors (or one normalized, one ...
16
votes
2answers
16k views

How can I convert a mouse click to a ray?

I have a perspective projection. When the user clicks on the screen, I want to compute the ray between the near and far planes that projects from the mouse point, so I can do some ray intersection ...
3
votes
2answers
3k views

Decomposing a concave mesh into a set of convex meshes

I'd like to be able to decompose a concave mesh into a set of convex meshes for 2 reasons: Transparent rendering Physics shapes Is there an algorithm that takes a set of triangles (concave) as ...
0
votes
1answer
644 views

Issues with Sine Wave Generation and Rotation

I'm working on generating objects in sine wave that lets you specify parameters that are start x, end x, start y, and end y position. Below is the method that I used to generate the debris void ...
1
vote
0answers
117 views

How can I keep vertex order the same on every Instantiate()?

While trying to resolve another question, I have discovered that if I Instantiate() from a prefab, the order of the mesh vertices (and therefore triangles) is inconsistent between instances. This is ...
1
vote
1answer
61 views

Algorithm that cover one mesh by another mesh

Suppose I have two meshes (Let call me first MeshShirt and second - MeshBody) Meshes are aligned (if i render both MeshShirt "covers" MeshBody). But some parts of the body are not "under" the ...
0
votes
1answer
267 views

Formula to measure uv-mapping distortion

Does anyone know a simple way of calculating (offline) the amount a texture is distorted when mapped to a triangle like the following? Vertex Position UV Coordinates A (Ax, Ay, Az) (...
1
vote
1answer
250 views

Chamfered cube geometry generator

I'm trying to create a geometry generator for a "Chamfered Cube". I've got the vertices working, but I'm stuck with creating the faces. I don't really know how I could re-arrange my algorithm to ...
0
votes
0answers
119 views

Calculation technique for 2D inertia tensors?

Just wondering what the techniques are out there. It's only 2D so I figured there'd be a good chance for there to be a "one size fits all" solution out there that's essentially an analytical solution. ...
0
votes
1answer
373 views

Given seams, how do I unfold a mesh?

If a user marks a seam on a mesh, how do 3D modelling programs (like Blender or Maya) unfold the mesh on to a 2D surface? I can only find papers trying to automate the seaming for you. Given user-...
2
votes
1answer
4k views

How do I find the circumcenter of a triangle in 3D?

I want to find the circumcenter of a triangle. Wolfram only shows how to find the circumcircle of a triangle in R2. How can I find the circumcenter of a triangle in R3?
1
vote
2answers
205 views

How to find the points of intersection of two OBBs

In my game I need to be able to find the points of intersection between two OBBs. I'm using Separate Axis Theorem to check if there's an intersection and get the penetration vector if there is one. ...
2
votes
1answer
450 views

How to access Maya Bonus Tools 2012 in Maya 2014

I have been trying to use the paint geometry tool for Maya 2014 but it isnt showing up. I downloaded Bonus Tools 2012 and installed it. Where can I find this tool in Maya 2014?
1
vote
1answer
477 views

In a TPS, how to aim bullets to the direction the camera is pointing, but make the shooting from the player?

(In C#/XNA.) I mean, I can't find an answer nowhere. I'm trying to learn how to make a Third Person Shooter, especially like the one I found in a game called "M.A.R.S.", from Epic Games. I don't want ...
2
votes
1answer
99 views

Distort a quad with a World Matrix

Is it possible to distort a quad multiplying its vertices by a specific world matrix? See the picture to understand what kind of distortion I need: Please note, that the quad is in 3d space and I ...
2
votes
2answers
48 views

Calculating angle a segment forms with a ray

I am given a point C and a ray r starting there. I know the coordinates (xc, yc) of the point C and the angle theta the ray r forms with the horizontal, theta in (-pi, pi]. I am also given another ...
0
votes
3answers
157 views

Calculating the center of a turning circle

I'm trying to understand how to calculate the midpoint of a turning circle. In the attached picture, my unit is at location U. I want to compute the trajectory of the unit as it turns toward the ...
3
votes
1answer
145 views

How can I animate characters' static-geometry eyes?

Here's a Nintendo example: Specifically, the animation of the pupils seems not to animate the geometry. How is this done?
0
votes
1answer
115 views

How to calculate “real” distance between cursor and away object?

I don't really know how to formulate the title, but the problem is the following: I'm using a scripting language called "SQF" which has been created by a company named "Bohemia Interactive" (no, I do ...
1
vote
1answer
68 views

Rotating a square rendered on a Bitmap

I'm writing a Software Renderer for fun/learning. Basically, it's just a giant array of integers which contain hexadecimal values (representing colour) that are rendered to the screen.... int ...
3
votes
2answers
389 views

How to calculate direction from initial point and another point?

I'm making a simple game where I shoot things from a certain point on screen (A). I tap the screen and shoot the projectile from initial point(A) to the tap point(B). But I want the projectile to ...
9
votes
3answers
2k views

How do I translate a spherical coordinate to a Cartesian one?

Could someone point me in the right direction as to how this might be achieved? 3D math / geometry often throws me. I'm looking for something like this (ideally in C#): public Vector3 ...
1
vote
1answer
107 views

How do I combine matrix transformation with non-uniform screen scaling in Flash?

I'm using a Flash transformation matrix for affine transformation. I have a rectangular image being rotated and scaled (in 2D). There are two sets of scaling variables, ScreenScaleX and ScreenScaleY, ...
1
vote
1answer
31 views

Error in plane transformation

I have a bunch of coplanar points, who sit on plane P. I want to translate the plane to Q with the points upon. Here is what I do: I take three points from P, say a, b, c. Their centroid is denoted ...
0
votes
1answer
64 views

Picking a local origin as the centroid of given three points in 3D

Given three points non-collinear P, Q, R in 3D, I need a generic method to generate x', y', z' unit vectors that behave like origin of local coordinate system. x' and y' vectos should be on the plane ...
1
vote
1answer
101 views

Point in Polygon, Ray Method: ending infinite line

Having a bit of trouble with point in polygon collision detection using the ray method i.e. http://en.wikipedia.org/wiki/Point_in_polygon My problem is I need to give an end to the infinite line ...
0
votes
1answer
52 views

Geometry design and buffers

I'm making some tests with rendering stuff and I'm wondering how to design my Geometry class. For the moment, here is how I do: Init: Stock array with positions, array with colors, array with ...
3
votes
2answers
306 views

How to make a projectile align correctly with the entity that shot it

I'm developing a 2D game. In the game, all entities can rotate 360 degrees. Each entity holds an angle value, and every frame it is drawn rotated around it's center by it's current angle value. For ...
3
votes
1answer
546 views

Explain this line segment intersection code

I've been reading this article on pathfinding over polygon meshes using line-of-sight, and in the article are several code snippets. One of them, the one I'm trying to understand, is a simple function ...
1
vote
1answer
226 views

XY Location scaling with varying density screens

I have a phone with resolution H=1280,W=720,Density=2 I have a tablet with resolution H=1216,W=800,Density=1.331 I drew a rectangle on my phone with corners Left,Top (-1.6,1.55), Right,Bottom (1.6,-1....
8
votes
1answer
2k views

Tessellation vs Geometry Shader

Correct me if I'm wrong, but both the Geometry Shader and the Tessellation Shader jobs are to generate vertices in the Graphic Pipeline. What I would like to know is how they are different and when ...
1
vote
1answer
96 views

Reflection velocity

I'm trying to get a moving circular object to bounce (elastically) off of an immovable circular object. Am I doing this right? (The results look right, but I hate to trust that alone, and I can't ...
21
votes
4answers
3k views

Is there a 3D equivalent of hex tile maps?

Probably the biggest advantage of a hex-based versus square-based map tiling is that the center of each hex has the same distance to all its neighboring hexes. Is there a similar shape that tiles this ...
1
vote
1answer
447 views

How do you make a bullet ricochet off a vertical wall?

First things first. I am using C# with XNA. My game is top-down and the player can shoot bullets. I've managed to get the bullets to ricochet correctly off horizontal walls. Yet, despite using similar ...
3
votes
1answer
2k views

Sphere-Sphere intersection and Circle-Sphere intersection

I have code for circle-circle intersection. But I need to expand it to 3-D. How do I calculate: Radius and center of the intersection circle of two spheres Points of the intersection of a sphere ...
3
votes
2answers
352 views

Find the next cell in a grid from a point and direction

I'm trying to solve a very simple problem but I'm unable to come-up with an efficient solution so far. What I'm really trying to do is voxelize triangles in a three dimensional environment but I'll ...
2
votes
2answers
186 views

Connecting two arbitrary points with 2 lines

DEFINITIONS: Any "Point (x, y)" mentioned below is really the bottom left coordinates of a 1 unit by 1 unit rectangle. A "Line" is a defined as a rectangle that is either 1 unit tall and 1 unit or ...
3
votes
3answers
452 views

Throwing a ball and estimating its path using a Physics engine

The problem: A player entity wishes to throw a ball from a known position with a known initial velocity. The surrounding environment contains physical objects that can alter the trajectory of the ball....
11
votes
4answers
703 views

How can I find the largest sphere that fits inside a frustum?

How do you find the largest sphere that you can draw in perspective? Viewed from the top, it'd be this: Added: on the frustum on the right, I've marked four points I think we know something about. ...
1
vote
1answer
113 views

Calculate diameter of sphere large enough to encompasss a frustum

I'm attempting to speed up box-to-box collision checks by first testing if two spheres large enough to encompass each (respectively) would collide (because I'm using separating axis theorem and it's ...
1
vote
2answers
549 views

Find closest point from an origin, in a mesh

I want to do something similar to a raycast. With a raycast, you can set an origin and a destiny, and check where the ray collides with something but only with a line. What I want to do, is given an ...
3
votes
1answer
781 views

Converting between Spiral Honeycomb Mosaic and axial hex coordinates

There seems to be quite a lot of logic in dealing with hexagonal grids using a system of axial coordinates like the one described here. In doing some reading about hex grids, though, I ran across the ...
2
votes
1answer
385 views

Moving an object toward another object on sphere knowing their quaternions

I have a sphere centered in world origin. On the sphere surface I have two objects and I know their quaternions (rotation around sphere). Currently my movement works on Vector2 inputs (cannot change ...
2
votes
2answers
146 views

How can I test if a point is behind a polygon in 2D?

In order to improve the performance of my visibility graph generator I am trying to figure out the following. Given the image below; is there a way to find out if a point is 'behind' the polygon? For ...
0
votes
0answers
63 views

Rasterizing euclidean planes

I'd like to visualize a BSP tree. To do this, I need to project an arbitrary euclidean plane onto a projection plane. I was thinking about calculating the intersections of the plane with the viewing ...
10
votes
1answer
1k views

How do I make a curved surface out of rectangular blocks?

For a Peggle-like game, I want to make blocks that follow a curve, like this: The blocks would then disappear as the ball hits them. I managed to draw some horizontally, but I'm having trouble ...
0
votes
1answer
107 views

Best method for selecting points from a point set - path distance

having a big set of points and a polygonal path what is the best way to select a set of points that are at a certain distance or smaller from the path? Or do I need to iterate thru all points on each ...
0
votes
0answers
49 views

Java Angle Math: Calculate how near the player looks to an entity [duplicate]

I am programming a Minecraft Bukkit plugin and need a way to calculate an input number from 0 to 360 for displaying a custom compass / radar. So if the player directly looks at the object (shouldn't ...