Fractals/Computer graphic techniques/3D

Rendering

• API ( C++, JS ...)
• Backends (Renderer Back-End Architecture):
  • OpenGL 4.1+ for Linux, macOS and Windows
  • OpenGL ES 3.0+ for Android and iOS
  • Metal for macOS and iOS
  • Vulkan 1.0 for Android, Linux, macOS, and Windows
  • WebGL 2.0 for all platforms

Rendering

• image-order rendering ( CPU-based ray tracing )
• object-order rendering ( GPU-based rendering. Faster since we can apply the same instructions, but on different vertices in parallel.)

 "A single frame in Toy story 4 could take anywhere between 60 to 160 hours to render using CPU based ray tracing."Brendan Galea The Math behind (most) 3D games - Perspective Projection by  Brendan Galea

Elements

• mesh
• texture ( map )
• geometric transform
• pipline

3D graphics have more in common with vector graphics than with raster graphics. The content of an image is specified as a list of geometric objects. The technique is referred to as geometric modeling.

Rendering the scene = creating 2D image of 3D object/world

Light and shadow

• Lights and Shadows by Bartosz Ciechanowski
• Physically Based Rendering in Filament

3d still images

The task of a 3D graphics program is to turn the specification of a 3D environment to 2D pictures.

There are two ways to generate such pictures:

• real-time rendering (interactive graphics applications such as video games or simulations)
• non-real-time rendering ( non-interactive graphics applications such as film).

Programming languages for host programs ( CPU) using API

• C
• C++

Special APIs

• OpenGL
• WebGl
• Direct3D
• Vulkan
• OpenCl
• CUDA

programming languages for shader programs ( GPU)

• GLSL ( OpenGl)
• HLSL ( DirectX)
• Cg (NVIDIA's shading language)

Pipeline or workflow

3D Rendering

The 3D pipeline contains:

• a hardware pipeline ( main memory, CPU, a PCI Express bus, GPU, and GPU memory)
• a software pipeline

software pipelines:

• Host program on CPU ( The 3D programs that run on the CPU )
• Shader programs on GPU ( The bulk of the 3D data processing )

The job of the host program includes :

• Initialization
• Set up or reconfigure the 3D software pipeline
• Build shader programs
• Transfer shader programs to GPU
• Data management
• Load 3D data
• Process the 3D data
• Update 3D data
• Transfer the 3D data to GPU
• Send commands to GPU
• Process user inputs and update the 3D data

Shader programs:

• vertex shaders
• fragment shaders
• geometry shaders

Each APi has it's own pipeline

• 
  Pipeline OpenGL 1.0
• 
  Pipeline D3D11
• 
  Pipeline D3D 10

mesh

• MeshLab - the open source system for processing and editing 3D triangular meshes.

It provides a set of tools for editing, cleaning, healing, inspecting, rendering, texturing and converting meshes. It offers features for processing raw data produced by 3D digitization tools/devices and for preparing models for 3D printing.

Converting 2D images to 3D

• 2D fractals mapped onto a Riemann sphere

For height of each pixel one can use :

• distance to boundary : "I'm using the distance estimate method (DEM) as the basis of my height values. (inverted, the log, scaled and streched, etc.)" Duncan C
• fractional iteration values

3D to 2D

• project the points in 3D space into cylindrical surface that can be unwrapped, to a flat surface

video or animation made from 2D images

What is the difference between video and animation ?

Software used to do the conversion :

• answer on fractal forum
• commons help

parameter plane

One can make videos using :

• going along some paths on parameter plane ( for example internal and external rays )
• Poincaré half-plane metric for zoom animation
• zoom into parameter plane using automatic determination of Iteration Max number
• changing coloring scheme ( for example color cycling - Fractint)
• changing some parameters of algorithm, for example :
  • maximal iteration of escape time algorithm
  • bailout value

path

• straight line from c=-0.75+i to c=-0.75-i. It is mostly in the exterior of Mandelbrot set ( then Julia set is disconnected with no interior). There is only one point c=-0.75 where c belongs to the boundary of Mandelbrot set ( root point between period 1 and 2 hyperbolic components). In that point Julia set has interior ( parabolic ).
• from c=-2 to c=1.65 ( real slice of Mandelbrot set )
• around a circle centred at -1 and with a radius of 0.25
• around main cardioid
• parameter traces a circle centred at -0.29848658+0.65843271i and with a radius of 0.004. On the parameter plane, this does a circle around a point of the Mandelbrot fractal that is radiating 11 strands in a very loose spiral.
• races a circle centred at -1.57621921451761 and with a radius of 3.6 x 10^-10. On the parameter plane, this does a circle around a minibrot at that location without passing through the minibrot itself.