Questions tagged [mathematics]
Mathematics questions deal with the arithmetic, geometry, calculus, formulae and other calculations used in the development of a game.
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Difference between column- and row vector matrix multiplication (vector transform)
Let's say we have a 4-by-4 matrix \$A\$ which represents some transformation.
We can use this matrix to transform a vector in two ways.
\$Ax\$ by assuming \$x\$ is a 4-by-1 column vector.
\$xA\$ by ...
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Scale sprite between two points
I need to start a sprite at a scale .6 (scale1) at a y position 40 (yPos1). Knowing the end y position 560 (...
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How to work out the height of a point on a tilted surface?
I have a plane which gets tilted on the X and Z axis (y+ is the normal).
Given an X and Z coordinate and the X and Z rotation of the plane, how do I find out the height (Y) at that point?
I assume ...
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2
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Calculate current level and level requirements when only XP is being updated
I am trying to create a formula to calculate the players level based on his XP alone. The game currently only increments his XP after certain actions.
I have the formula for calculating the required ...
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Merge angle range
I have AngleRange class with define range to angles to detect if a angle is inside the range.
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Decide which scoring system to use and number of points to assign for new game [closed]
I am developing a new game and would like to know if anyone could point me in the right direction for deciding the type of scoring system to use for my new game as well as the number of points to ...
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Calculate line intersecting most points, based on random points in a grid
I have been struggling with a math issue for a game I've been developing. I am in need to find the best starting and ending point for a straight line so that it intersects most of the circles (the ...
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Drawing & transforming matrices upwards
I'm drawing a hierarchy of 3D objects in C# XNA where each objects has a transform that holds position, rotation and scale.
I get my expected results If I draw my objects from my root node in this ...
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Approximating a fourth point with a weighted average between three points?
Given three points \$p_1,p_2,p_3\$, how would one approximate the best positive weights \$(u, v, w)\$ such that \$u+v+w = 1\$ and that the distance between the new \$up_0 + vp_1 + wp_2\$ from \$p_3\$ ...
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Transform point while keeping other points offset
I have the following situation: I've got a box with its center of mass transform matrix that I'm obtaining from physics simulation, i.e. it keeps changing with time. I've also got two points (actually ...
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3D software-based engine projection issues
I have been writing a 3D soft-engine for a little while and I have gotten it a reasonable position but recently noticed a bug that I can't seem to solve. When I am rendering a few cubes as a test, if ...
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Timebased transition from start to end value
I'm trying to implement time line objects, the purpose of those would be to issue events at specific times. When and what is specified through objects called units, which is what you attach in the ...
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Hemisphere Projection
I came across the following segment of code that is supposed to project an image on a hemisphere:
...
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Calculate damage values from bullet velocity and size
I'm trying to make a top-down game using Javascript and Pixi which involves multiple different guns.
Instead of giving each gun an individual damage value, I wanted to calculate the damage by the ...
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Determine the z coordinate of a deformed plane based on uv (xy) coordinates
I am using a formula to turn the following texture
into what looks like two 3 dimensional planes
The formula I am using for the texture deformation is
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Perlin Noise' gradient
I'm having some problem understanding the Perlin Noise algorithm and none of the explanation I found go into this (probably obvious)detail.
From what function is the gradient on it? Is it from the ...
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How to handle edge cases for a cell divided multiplayer world?
The most common practice that I read about for overcoming floating point precision in video games with large worlds is by dividing the world into cells and load it with player's position and shift ...
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render text inside countries
I have a map of the world and I want to place text on top of each country. The text can be anywhere from 0 to 1000 symbols long, and can often be changed.
I'm looking for an algorithm to layout text ...
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LIBGDX Perspective Camera in an Isometric view?
how can I set a PerspectiveCamera to view the game in an isometric view? What kind of angle would I use, and how would I actually translate this into the code? Math ...
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Axis of affine transformation matrix
Let's say I have a right handed column major 4x4 transformation matrix. Can I safely assume (even though there exist non uniform scale) that first column is X axis vector, second column is Y axis ...
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Project 3d lines onto plane
I'm trying to wrap my head around coordinate projection, and can't seem to solve the problem I am having. Here is an illustration of it:
The cubes represent 3d space, and the 2 red lines represent ...
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how to create an outlined polygon with vector3 coordinates?
I have a set of vector3 coordinates and I use them to draw a polygon in another app, my question is: how can I calculate a second set of coordinates to make it look like the line is outlined.
in ...
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Calculate experience for each kill [closed]
I need a formula to calculate experience of players on each kill. It's based on the value of armor of the 2 opponents. For example if i kill the opponent and i've a total armor of 4000 gold and the ...
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Find the closest point on a ray
I've got a ray defined by P1 and P2, and then a target P3, and I want to find P4. How do I go about this? I've come to understand that I should use vector projection, but I can't get it to work. Any ...
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Finding the Distance between 2 Objects
I have 2 objects One Having a Transformation Matrix T1 and other Having Transformation Matrix ...
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Finding if 2 polygons intersect using clipper library
After realising my code was pretty inefficient at checking for polygon overlaps, I've turned to a mentioned library Clipper but finding it difficult to know hot to use it for this operation.
I am ...
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Finding when shapes overlap and lines intersect but exclude points/edges
I've been looking for a c# algorithm to help determine if shapes and lines intersect but want to exclude boundary overlaps. Here's an example:
My true problem is finding if polygons intersect but ...
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Snapping shapes together in game
I'm trying to work out how to snap shapes together the player may move around on a canvas.
As the square approaches the other object, I want to pull that shape in (given a certain proximity) and have ...
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Points inside a Polygon, failing for shapes with 0,0
I've been using an algorithm (http://wiki.unity3d.com/index.php/PolyContainsPoint) to tell me if a point is inside a polygon... in fact a few variants (here and here) but they all come back the same. ...
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Checking if shapes will tessellate
I'm trying to figure out where to start with getting code together to check if a shape tessellates.
An example:
Consider that the shapes cannot be rotated, just as-is. A 'compound' shape (as seen in ...
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Formula For Finding Out Price of Item? [closed]
I've been working on a game with a friend for a while now. I'm in charge of plotting most of the stats on the weapons.
Weapons have several attributes:
Four damage types: Base, Impact, Punct and ...
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Computing chance of winning when dealing with fuzzy numbers
Computing chance of winning in a one player and one enemy battle when using fixed numbers is quite easy; for example if we have these numbers:
Player : Attack : 5 - Health : 30 - Attack Interval : ...
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Problem with RGBA sampled shadowmap
I'm having a problem with the generation of a shadowmap that is converted to RGBA. The following glsl code is used to put the depth into the depthbuffer :
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Zobrist Hashing equivalent for Simple Knights Game with only 1 unique piece
I looked over the Zobrist hashing function used for getting a unique hash id of the board state in a chess game. https://en.wikipedia.org/wiki/Zobrist_hashing
Martin Fierz explains it very well in ...
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Parametric form of a cubic function
After researching about curves in computer graphics (splines in my case), I have come across something I did not know: Explicit functions like: \$y=x^2+2\$ are not the best way to interpolate between ...
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Why aren't regular quadratic and cubic splines used much in games?
After investigating a bit about splines and reading a bunch of docs, I have noticed regular quadratic and cubic splines are not used very much in games.
Splines using quadratic/cubic Bézier curves, ...
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RPG Formula - Attack and defense
I'm making a game and I'm struggling with the formula to calculate the real damage the player does. I have skills which can do for example 10 hits of 20% weapon damage each of a total of 200% damage. ...
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Scaling a rotated rectangle in a given direction
I'm facing an issue when trying to scale a rotated rectangle in a given direction.
In my context, the width and height of the rectangle are based on the texture size multiplied by a scale factor (...
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Time series for creating new events in a PVP game
This is more like a mathematical problem, but I guess this is the best place to ask it.
I am working on a PVP concept and I have the following problem. There is a "battle" between two players that ...
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Finding a tile number in a grid system
Hi I am trying to find the Tile number of a grid of tiles based on the Z and X coordinates.
Where the Z and X axis are potentially infinite in either direction how can i get the number of the tile, ...
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Aim assist (GoldenEye/Perfect Dark)
Anyone remember how the aim assist works in GoldenEye on n64? Where the gun model would point at an enemy if he's within a certain area in your field of view. I'm trying to do something like that but ...
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Why doesn't JavaScript's Math.cos function match this vector tutorial?
I'm following this MATHguide lesson on combining vectors and have reached this part:
Next, we need to convert their forces to horizontal and vertical components. Let's use k for Kim's vector and n ...
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Convert box to matrix
I have a box (non-rectangular cuboid?) and would like to convert it to a matrix such that when a point inside the box is multiplied by the matrix, a vector is returned that describes the relative ...
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Center of Image whose height, width and position are known
I have been struggling to find the center of an image(rectangle). I have following data with me:
width: w,
height: h,
position: (x,y)
My image is an object on ...
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cylindrical coordinate point in origin
I have a camera which has the following attributes:
pos (position of the camera in the scene)
look(either direction in which camera will face, or target vector)
up vector( y axis)
I am using ...
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clamp a 2D coordinate to fit within an ellipse
I need to clamp a 2D coordinate to fit within an ellipse.
Call of Duty: Modern Warfare 2 does something similar where capture points are translated from a 3D vector in the world to a 2D screen ...
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How to get the point of collision in Separating Axis Theorem?
I'm interested in the relatively precise point (not line) of collision for calculating angular velocity on impact for use in a impulse calculation. At first I thought, perhaps naively, that I could ...
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How to calculate move forward direction in Libgdx with Box2d body
I'm working on a game using Libgdx, I've create my world, bodies, fixtures etc. Everything is functional everything is working perfectly but the problem is my body just can left-right-up or down and I ...
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Approximating particles with with nebula
I have a 2d galaxy where each star is rendered a particle:
I'd like to approximate it with nebula, so that instead of seeing lots of tiny dots from afar, users will see lots smooth light in the area. ...
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How to get connected tiles in hexagonal grid system
I've been developing a game where a number of tiles can drag into a hexagonal grid background.
For some purpose I need to find the location of same tiles into an array and merge them.
Data Layer:
...