Spirula
GPU-accelerated function graphers in a web browser, both 3D and 2D.
This is a personal passion project. I couldn't find a 3D graphing calculator with satisfying 3D implicit surface rendering on the internet, so I decided to make one. I was inspired by raymarching demos on Shadertoy.
After my 3D implicit surface grapher received positive feedback from other people, I thought, why not extend the same equation parser and renderer to other types of math functions? Under this motivation, I developed the following function graphers:
- 3D implicit surface grapher
- Complex domain coloring grapher
- 3D complex domain coloring grapher
- Implicit curve grapher (for testing, not intended to be useful)
It is important to note that these function graphers are developed completely by my effort. Since I don't have much knowledge of advanced functions (especially the complex-variable ones, which I only found their graphs to be visually cool), I cannot guarantee the mathematical practicability and accuracy of these tools. If you have any suggestions or believe you are experiencing a bug, feel free to open an issue on GitHub.
The name "Spirula" comes from the name of a deep-ocean cephalopod mollusk that has distinctive spiral shells.
Features
The equation parser implements the following features:
- Function and variable definition
- Comments (start with a
#) - LaTeX preview
- Real-time shader generation
- Automatic differentiation
The 3D graphers implements the following parameters/features:
- Multiple shading modes
- Dark and light color themes
- Speed vs. quality control
- Lighting control
- Axes and grid
- Red highlight discontinuity
- Semi-transparent surface shading
- Anti-aliasing
Limitations
These tools have the following dependencies:
- WebGL 2
EXT_disjoint_timer_query_webgl2, an FPS counter will be shown when availableEXT_color_buffer_float, currently not required but is very likely a dependency in the future
- MathJax 3, required for rendering equation preview
These tools have the following known issues:
- Incompatibility across devices for functions with overflow and NaN
- Reduced quality when rendering surfaces with transparency
- Ambiguity in resolving functions with conflicting parameter names
Features that may be implemented in the future:
- Iterative refinement to improve rendering quality
- Code generation (GLSL, C/C++, NumPy, MATLAB, LaTeX, etc.)
- Exporting mesh-based 3D models
- Vector arithmetic
- Mathematically-defined custom colors
- Variable sliders
- Better expression editor (highlighting, bracket matching, etc.)
- More viewport control parameters
- More domain coloring parameters for complex graphers
<iframe>embed for webpages- Graph sharing via URL
- Parametric surface grapher
Gallery
Complex domain coloring
Complex domain coloring in 3D
A sextic algebraic surface
The Burning Ship fractal
An algebraic star surface with transparency
Complex 3D plots of the Gamma function and the Riemann Zeta function
