NURBS Mathematics

Non-Uniform Rational B-Splines - Industry standard for representing freeform curves and surfaces. Full support for rational and non-rational B-splines with arbitrary degree, knot vectors, and weight control.

• ✓ Cox-de Boor recursive evaluation
• ✓ Knot insertion & refinement algorithms
• ✓ Degree elevation/reduction
• ✓ Homogeneous coordinate arithmetic

Geometric Continuity

G0, G1, G2 Continuity Control - Precise control over surface transitions. G0 (position), G1 (tangent), and G2 (curvature) continuity for Class-A surface quality in automotive and industrial design.

• ✓ Quintic Hermite interpolation for G2 blends
• ✓ Cross-boundary derivative matching
• ✓ Tangent magnitude and curvature scaling
• ✓ Visual curvature combs for quality verification

Class-A Surface Modeling

Automotive-Grade Aesthetics - Tools specifically designed for high-quality aesthetic surfaces. Used in automotive, aerospace, consumer products, and industrial design where visual quality is paramount.

• ✓ Coons patch interpolation
• ✓ N-sided patch with RBF smoothing
• ✓ G2 blend surfaces (quintic B-splines)
• ✓ Surface fairness optimization

Curvature Analysis Tools

Real-Time Quality Feedback - Zebra stripe analysis, Gaussian/mean curvature visualization, highlight line reflection. Industry-standard tools for evaluating surface quality and detecting discontinuities.

• ✓ Zebra stripe (reflection line) analysis
• ✓ Gaussian & mean curvature maps
• ✓ Curvature comb display
• ✓ Isophote/highlight line visualization

Reverse Engineering

Scan-to-CAD Pipeline - Convert point clouds and meshes to editable NURBS surfaces. Essential for reverse engineering, digitized prototypes, and legacy part reconstruction.

• ✓ Mesh-to-NURBS surface fitting
• ✓ Point cloud approximation
• ✓ Adaptive knot placement
• ✓ G0/G1 tolerance-driven refinement

Advanced Meshing

Manufacturing-Ready Output - Generate high-quality triangle/quad meshes for 3D printing, FEA simulation, and CNC machining. Smart meshing algorithms preserve geometric features.

• ✓ Adaptive surface tessellation
• ✓ Quad-dominant mesh generation
• ✓ Triangle-to-quad conversion
• ✓ STL export for 3D printing

High-Performance C++ Kernel

Hand-optimized computational geometry engine written in modern C++17. Eigen3 library for vectorized linear algebra operations. Memory-efficient data structures and cache-aware algorithms for real-time performance on large datasets.

Python GUI Layer

Professional desktop interface built with Tkinter and matplotlib for 3D visualization. Python-C++ bridge via ctypes FFI enables rapid prototyping and scripting automation while maintaining kernel performance.

Numerical Precision

IEEE 754 double-precision floating-point throughout. Configurable tolerance contexts for geometric operations. Robust handling of degenerate cases, numerical instabilities, and edge conditions in CAGD algorithms.

Extensible Plugin System

Open architecture allows custom curve/surface types, new operations, and workflow automation. Python scripting API exposes kernel functions for batch processing and specialized applications.

Native File Format

JSON-based .cadmvp file format stores complete geometric hierarchy. Human-readable for version control, scriptable for automation, lossless for round-trip editing. Import/export for industry standards (IGES, STEP) planned.

Cross-Platform Support

Runs natively on Linux and Windows. Same feature set on both platforms. No cloud dependencies—all computation happens locally for data security and offline capability.