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# The Use of Geometry in Video Game Design

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## Steven Claffey

on 17 October 2014

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#### Transcript of The Use of Geometry in Video Game Design

The Use of Geometry in Video Games
Isometric Graphics
Isometric Graphic Design
The Use of Differing Viewpoints
Isometric Graphics use changing angles of view to create Faux 3D. An example of this is in Pokemon, as indicated by the following picture
Isometric Graphic Design can be used to create an object that appears to be 3D, but is not. Isometric projection is the process of tilting a certain axis to change the angle at which an object is viewed. Direct your attention to the picture from Pokemon Black/White
Landscaping and Terrain Design
One Word: Polygons
Everything in Games is made of polygons
The characters, buildings, the terrain, even the background are all polygons.
Everything in this picture is made up of polygons, set in certain places at certain angles, such as the trees. the trees are made up of tiny triangles, or cones, or any sort of very small polygons/ polyhedrons set at certain angles
In the above picture, you see the character climbing a rock wall. Due to how it's programmed the character may only be able to climb a wall with a 5 degree angle of depression and a crack between two squares, as long as there are no polyhedrons sticking more than 7 feet out of the wall. because of the programming of the game, the character can leap for 4 feet between 2 points horizontally, and as the angle decreases, so does the distance the character can leap. This also works in negative.
As an example, the player can leap certain distances with a certain angle of trajectory.A horizontal leap has a 4 ft. distance at an angle of 180 degrees, so, completely flat. At 90 degrees, a vertical leap, the character can jump 2 feet. however, the same principle applies to negative leaps. At an angle of 270, a vertical drop, the player can jump 8 feet.
180 degrees=4ft. 180degrees-90 degrees=2ft. 180 degrees+90 degrees=8ft. 180 degrees+180 degrees=4ft.
As well as being used to create textures and terrain in video games, geometry is also used to create the "sprites." "Sprites" are the collective referral to the character's image.
Sprites can be incredibly simple or incredibly complex. The tiny rocket-ship from Galaga is classified as a sprite. An example of a very complicated sprite could be many things from many video games, especially modern games. A useful example would be "Alduin" from The Elder Scrolls V: Skyrim
These three images are sprites; beings that are simply made up of polygons. From left to right, they grow progressively more complicated, but they are simply made up of a certain amount of polygons.
Geometry is used throughout video game design in controlling how the player's view of the game through isometric graphics, how the terrain is designed and textured through the use of polygons, and how the character moves through the game through the use of arcs and angles.
Through the design of terrain and objects, polygons, and therefore, geometry are used in video game design
Despite being used in how the world is built, geometry also plays a part in how the game is actually played
A large part of video game design is calculating how the player moves. This can be from how many units the character moves at the click of a button to where a bullet ricocheted around a corner will hit an alien moving in a straight line.
One example would be from Assassin's Creed: Revelations
The player performs a leap onto a hanging object that then swings, launching the player. However, many variables can affect the effectiveness of this maneuver.
For example, if the player runs in a straight line at 8mph, then the player swings on an arc with a measure of 150 degrees to be launched 10 feet from the rim of the arc.
8mph+150 degrees= 10 ft.
Of course, this isn't the only game where geometry is used to determine how the character moves.
In any games where one can move in 3 dimensions, the designers must calculate how many degrees the click of a button will turn you, or how many units the player will move if a stick is pressed.
Game designers use many forms of math, not just geometry, but geometry is a large part of what makes the game be a game, not just lines of code.
How Geometry has been historically used.
Math has been used historically in video game design, even back in Pong (1972), with angles. As processing power on computers has advanced, designers have become capable of using more and more complicated math to create more advanced video games.
Perspectives on the use of geometry in video game design
The use of geometry and other forms of math in video game design are ignored by the average gamer, but in reality, game design is heavily dependent on math, especially on geometry.
The viewpoint is now much lower behind the character to provide a more scenic view, instead of a character-focused view. This changed view was created by moving down on the Y axis by about 22.5 degrees, while staying the same on the X and Z axes.
As you can see, the game provides a viewpoint from over the character, but on an angle as well as on an angle behind the character. However, the angle can change to provide different views as shown by the following picture.
Polygons are closed plane figures with at least 3 straight lines.
The points on the graph above represent the different camera angles throughout the game, constantly alternating between those three points and many between them. If a line were drawn from the center to each point, the angle between each of the lines would be about 22.5. Top point=90. First point= 67.5. Middle point= 45. Third point= 22.5. Bottom point=0
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