Geometry and God have often been intertwined with many seeing the structure of the universe as a manifestation of divine design. Ancient cultures, from the Greeks to the Egyptians, viewed mathematics and geometry as sacred knowledge, revealing the underlying order and purpose of existence. In this sense, geometry serves not just as a mathematical discipline but as a way to contemplate the divine order of the universe.
3D Modeling and Meshes
- In most 3D games, characters, environments, and objects are built using polygons, which are basic geometric shapes like triangles and squares. These shapes are used to create 3D meshes that define the form of objects and characters.
- More complex objects are made up of many smaller polygons arranged in specific ways, allowing for the representation of curves, smooth surfaces, and intricate details.
Collision Detection
- Geometry is essential in determining how objects interact with each other in the game world. Collision detection involves using geometric shapes like spheres, boxes, or even more complex meshes to determine if objects are touching or intersecting.
- This is crucial for player movement, interactions with the environment, and handling things like shooting, jumping, or character-environment interaction.
Lighting and Shadows
- The way light interacts with surfaces in a video game world is rooted in geometry. Ray tracing, for instance, uses mathematical geometry to simulate the way light reflects, refracts, and casts shadows. This makes environments appear more realistic.
- Shadows are cast depending on the geometry of objects and their relationship to light sources.
Pathfinding and Navigation
- Many games require characters or enemies to navigate complex environments. Pathfinding algorithms use geometry to calculate the best route between two points, avoiding obstacles and taking into account terrain features.
- Common methods include A* (A-star) algorithms, which rely on geometric grids to map out paths.
Camera and Viewpoint Calculations
- The camera in a 3D game relies heavily on geometry to determine the player’s viewpoint, perspective, and how the world is projected onto the 2D screen.
- Field of view, depth perception, and perspective are all grounded in geometric principles, affecting how players experience the game world.
Physics Simulations
- Video games often simulate physics using geometry, especially for objects that need to interact realistically. The trajectory of a thrown object, how a ball bounces off a wall, or how characters move based on forces like gravity all rely on geometric calculations.
- Complex simulations like ragdoll physics or vehicle handling use geometry to calculate movement and forces applied to objects in real-time.
Level Design
- When designing a game level, the layout of rooms, corridors, and spaces is fundamentally a geometric exercise. Designers think in terms of the flow of space, scale, and proportion to create engaging and functional environments.
- Many games feature puzzles or challenges that require understanding geometric concepts, such as rotating objects, fitting shapes together, or navigating mazes.