3D render engine in Java Project

Description of the project

Create the three sides of your figure, add them to the list, run, and... here's your 3D visualization!

Project structure

5 possible iterations, from simple to complex:

• Orthographic projection (top-down view)
• Horizontal movement (left to right)
• Full 3D rotation and translation
• color assignment
• Depth-based rendering using a Z-buffe

Render logic

Each vertex is represented as a vector A = [aₓ, aᵧ, a𝓏]. To apply rotation, the vector is multiplied by rotation matrices. Matrix multiplication follows the associative property:

$$ \text{Rotation XY} = \begin{bmatrix} \cos\theta & -\sin\theta & 0 \\ \sin\theta & \cos\theta & 0 \\ 0 & 0 & 1 \end{bmatrix} $$

$$ \text{Rotation YZ} = \begin{bmatrix} 1 & 0 & 0 \\ 0 & \cos\theta & \sin\theta \\ 0 & -\sin\theta & \cos\theta \end{bmatrix} $$

$$ \text{Rotation XZ} = \begin{bmatrix} \cos\theta & 0 & \sin\theta \\ 0 & 1 & 0 \\ -\sin\theta & 0 & \cos\theta \end{bmatrix} $$

examples: (AT₁)T₂ = A(T₁T₂)

Moving the mouse on the x or y axis will trigger the listener to update the pixels.

The Z-buffer

To manage visibility and occlusion, the engine uses a Z-buffer. This is a 2D array that stores the depth value of the closest triangle rendered at each pixel.

• At initialization, the Z-buffer is filled with a maximum depth value.
• During rasterization, each triangle fragment is compared against the current depth value at its pixel.
• If the fragment is closer to the camera, the Z-buffer and pixel color are updated.
• If it is farther, the fragment is discarded. This technique ensures that only the front-most surfaces are visible, eliminating the need for manual geometry sorting. The Z-buffer is a standard feature in modern rendering pipelines and is essential for producing accurate and realistic 3D scenes.