About

In high-precision industries such as additive manufacturing, aerospace modeling, and game engine optimization, the integrity of a 3D mesh is paramount. A visual inspection is rarely sufficient. This tool serves as a comprehensive Geometric Verification Environment, allowing engineers and artists to dissect the mathematical properties of Wavefront OBJ files before they enter the production pipeline.

Unlike standard viewers that merely render pixels, this system calculates the physical properties of the object. It computes the Signed Volume using the divergence theorem, ensuring that the mesh represents a closed, watertight manifold suitable for 3D printing. It analyzes the distribution of normals n to detect shading artifacts and inverted faces.

The rendering engine utilizes a custom PBR-Approximation Shader (Physically Based Rendering), simulating the interaction of light with materials ranging from dielectric plastics to conductive metals. This allows for immediate visual validation of surface topology without the overhead of heavy desktop software.

Formulas

To calculate the volume of an arbitrary mesh, we treat the mesh as a boundary of a solid. Using the Divergence Theorem, we can convert the volume integral into a surface integral. For a triangular mesh, this simplifies to summing the signed volumes of tetrahedrons formed by each triangle and the origin:

Vol = 16 faces∑i=0 (p₁ ⋅ (p₂ × p₃))

Where p₁, p₂, p₃ are the vector coordinates of the triangle vertices. The sign of the result indicates the winding order (orientation). A negative volume usually implies inverted normals.

For lighting calculations, the Lambertian Diffuse term is combined with a Blinn-Phong Specular term:

I = k_d(L ⋅ N) + k_s(N ⋅ H)^α

Reference Data

Metric	Symbol/Formula	Engineering Significance	Unit Dimension
Polyhedron Volume	V ≈ N∑i=1 (p_i ⋅ n_i)Area_i3	Determines material usage for casting/printing. Only valid for closed manifolds.	units³
Surface Area	A = ∑ 0.5 × \|AB × AC\|	Critical for coating, painting, and drag coefficient estimation.	units²
Euler Characteristic	χ = V − E + F	Topological invariant. χ=2 implies a simple closed sphere-like surface.	Integer
Vertex Normal	n_v = norm(∑ n_face × θ_face)	Smoothed lighting direction. Weighted by the angle of incident faces.	Vector
Aspect Ratio	AR = l_longest / h_shortest	Indicates triangle quality. High AR (>100) causes rendering artifacts (slivers).	Ratio
Memory Footprint	M ≈ N_v × 32 bits	Estimates GPU VRAM usage for the geometry buffer.	Bytes

Frequently Asked Questions

The browser environment has a strict memory limit (heap size). For files >100MB, the parser uses a chunked processing approach to prevent the UI from freezing, but extremely large CAD exports (5M+ polygons) may still crash the WebGL context depending on your GPU's VRAM. We recommend decimating such meshes in external software first.

A negative volume indicates that the "Winding Order" of your vertices is clockwise, or the normals are pointing inwards. In 3D space, this effectively means the object is inside-out. You can ignore the sign for the magnitude, but for 3D printing, you must flip the normals.

No. All processing occurs locally within your browser's Sandbox (Client-Side). Your intellectual property never leaves your device. The "Save Snapshot" feature simply dumps the canvas pixel buffer to a local PNG file.

A non-manifold edge is an edge shared by more than two faces (e.g., a T-junction or internal wall) or an edge shared by zero faces (a loose wire). These are mathematically invalid for defining a solid volume and will cause slicing errors in manufacturing.