# Draft High-level Architecture


## Positioning and relation to existing libraries (Nice To Have but maybe to much)
ConformalLab++ is not intended to replace established geometry processing libraries such as CGAL, libigl, or Geometry Central. Instead, it acts as an experiment-friendly pipeline layer on top of existing data structures and algorithms provided by these libraries.

The project revives the ideas and algorithms of the original ConformalLab by Stefan Sechelmann in a modern C++ setting, making them easier to combine with contemporary mesh libraries (e.g. Geometry Central for intrinsic quantities and operators) and to reuse in new experimental setups.

In practice, ConformalLab++ focuses on:

+ a clear, declarative pipeline description for conformal and Möbius-based mesh experiments,

+ a unified halfedge-based UniversalMesh representation plus optional alternative representations,

adapters and plugin units that wrap robust external implementations where appropriate (e.g. CGAL-based repair or reconstruction, Geometry Central–style discrete geometry operators, or libigl functionality) instead of reimplementing them.



## High-level geometry pipeline
The following diagram outlines the planned high-level pipeline for ConformalLab++. It shows the rough division into preprocessing, processing, and postprocessing. In preprocessing, various input types are first converted into a universal representation (half-edge mesh) via adapter layers and any necessary preprocessing steps. From there, they are processed by the various core processors units and then either exported or visualized in postprocessing, with minor optimizations as necessary.

```mermaid
graph TD
    A1["Explicit<br/>(OBJ, PLY, STL)"]
    A2["Implicit<br/>(SDF, Formulas)"]
    A3["Parametric<br/>(NURBS, Curves)"]
    A4["Procedural<br/>(Noise, L-Sys)"]
    ADAPTER1["Input Adapter <br/>(Convert to Universal Represenation)"]
    PREPROCESSING["Preprocessor <br/>(refined triangulation etc.)"]
    EXT["EXTERNAL LIBRARIES<br/>(Plugin System)<br/>- CGAL"]
    UNIVERSAL["UNIVERSAL REPRESENTATION FORM<br/>(HalfEdge Mesh Interface)"]
    EXPORT_ADAPTER["Export Adapter Layer"]
    PROCESSING["PROCESSING CORE LAYER"]
    OPT["Optimization<br/>- Decimation<br/>- Denoising<br/>- Remeshing"]
    ALGO["Algorithmic<br/>- Boolean Ops<br/>- Smoothing<br/>- Hole Filling"]
    OTHER["Other<br/>- Custom Algos<br/>- Transforms<br/>- Filters"]
    POSTPROCESSING["POSTPROCESSING <br/>(refined triangulation etc.)"]
    EXPORT["Export Formats<br/>- OBJ<br/>- PLY<br/>- STL<br/>- Custom"]
    VIZ["Visualization<br/>- OpenGL<br/>- QT<br/>- Screenshot"]
subgraph PRE[PREPROCESSING]
    A1 --> ADAPTER1
    A2 --> ADAPTER1
    A3 --> ADAPTER1
    A4 --> ADAPTER1   
    PREPROCESSING <-->ADAPTER1
end
    EXT <--> UNIVERSAL
    UNIVERSAL --> PROCESSING
    UNIVERSAL --> EXPORT_ADAPTER
    ADAPTER1 <--> EXT
    ADAPTER1 <--> UNIVERSAL
    OPT --> UNIVERSAL
    ALGO --> UNIVERSAL
    OTHER --> UNIVERSAL
subgraph CORE[PROCESSING ]
    PROCESSING --> OPT
    PROCESSING --> ALGO
    PROCESSING --> OTHER
end
subgraph POST[POSTPROCESSING]
    EXPORT_ADAPTER <--> POSTPROCESSING
    EXPORT_ADAPTER --> EXPORT
    EXPORT_ADAPTER --> VIZ
end
    style UNIVERSAL fill:#90EE90,stroke:#000,stroke-width:3px,color:#000
    style PREPROCESSING  fill:#87CEEB,stroke:#000,stroke-width:2px,color:#000
    style POSTPROCESSING fill:#87CEEB,stroke:#000,stroke-width:2px,color:#000
    style PROCESSING fill:#87CEEB,stroke:#000,stroke-width:2px,color:#000
    style EXT fill:#DDA0DD,stroke:#000,stroke-width:2px,color:#000
    style ADAPTER1 fill:#FFB347,stroke:#000,stroke-width:2px,color:#000
    style EXPORT_ADAPTER fill:#FFB347,stroke:#000,stroke-width:2px,color:#000
```
All external inputs (file-based, implicit, parametric, procedural) are first converted by an spezfic input adapter into a single universal  interface, which is the canonical internal representation used by the processing stages. The processing core units operates on this universal representation and can use external libraries via a plugin-like extension, while results are passed through an export adapter to file formats or visualization frontends.


## Three-stage processing pipeline
The geometry processing pipeline in ConformalLab++ is structured into three main stages, all operating on the same universal mesh representation.

### Preprocessing
Converts all external inputs (files, analytic models, procedural sources) into the canonical half-edge mesh form.

Performs optional cleaning and normalization (e.g. fixing degeneracies, rescaling, enforcing orientation).

Guarantees that downstream stages see a well-formed, consistent mesh (or fail early with clear errors).

### Processing (core processing units)

Runs one or more core processing units in sequence on the canonical mesh.

Each unit takes a mesh of the same type as input and produces a mesh of the same type as output (possibly with enriched attributes).

Examples: remeshing, conformal parameterization, smoothing, boolean operations, experiment-specific transforms.

Each core processing unit conceptually has the shape UniversalMesh -> UniversalMesh, but units also declare:

+ Preconditions: requirements on the input mesh (e.g. triangulated, manifold, oriented, specific attributes present).

+ Capabilities: guarantees on the output mesh (e.g. remains manifold, produces curvature attributes, preserves boundary).

A simple example:

+ RemeshingUnit

  + Preconditions: triangulated, manifold, oriented

  + Capabilities: triangulated, manifold, vertex positions modified, edge count changed
 
Pipeline composition is valid if, for every adjacent pair of units, the capabilities of the previous unit satisfy the preconditions of the next unit.


### Postprocessing

Adapts the processed mesh for external consumption: export to file formats, visualization, analysis tools.

May attach or convert attribute data (e.g. colors, scalar fields, experiment results) into a format suitable for rendering or further tools.

Does not change the core topology or semantics of the processed mesh, only its representation for the outside world.

This structure makes it easy to reason about where data enters, is modified, and leaves the system, and keeps experimental algorithms clearly separated from IO concerns.

## Role of the universal mesh representation
The universal mesh representation (a half-edge mesh interface) is the shared contract between all pipeline stages.

### Single input/output type
Every core processing unit exposes the same function shape conceptually:
UniversalMesh → UniversalMesh.
This allows units to be chained in arbitrary order as long as their preconditions on the mesh are satisfied.

### Local, topology-aware access
The half-edge structure encodes vertices, halfedges, faces, and their adjacency relations, which is essential for typical geometry operations (e.g. local neighborhood queries, traversal, edge flips).

Algorithms do not need to know where the mesh came from (file vs. analytic vs. procedural); they only rely on this uniform interface.

### Extensibility via attributes
The universal mesh may carry extensible per-vertex, per-edge, and per-face attributes (e.g. UVs, curvature, experimental scalar fields).
Core units can read and write these attributes while still conforming to the same mesh type, enabling complex pipelines without changing the central data structure.



Because all processing units speak the same “mesh language”, you can build pipelines like:

```bash
Preprocessing
  -> RemeshingUnit
  -> ConformalMapUnit
  -> ExperimentSpecificFilter
  -> Export/Postprocessing
```
without changing the basic function signature or the surrounding infrastructure, only by reordering or swapping units.


## Declarative pipeline descriptions (Nice To Have but maybe to much) 
ConformalLab++ optionally supports a lightweight YAML-based description format for experiments.
A pipeline consists of an input adapter, a sequence of steps (core processing units), and an output adapter. Each step can specify params as well as structural constraints via require and provide keys. A pipeline is considered valid if, for every step, all require conditions are satisfied by the accumulated provide and expect constraints of previous steps

```yaml

pipeline:
  name: basic_conformal
  input:
    adapter: obj_reader
    source: data/bunny.obj

  steps:
    - id: clean
      unit: repair_soft_clean
      params:
        mode: soft
      require:
        representation: UniversalMesh
        triangulated: true
      provide:
        triangulated: true
        manifold: null

    - id: param
      unit: conformal_parameterization
      params:
        method: cauchy_riemann
      require:
        triangulated: true
        manifold: true
      provide:
        attributes_add: [uv]

  output:
    adapter: gltf_writer
    target: out/bunny.glb

```   
Each unit may declare a require section describing what it needs from its input (e.g. representation, triangulated, manifold, required attributes) and a provide section describing what it guarantees on its output (e.g. still triangulated, now manifold, adds a uv attribute). Pipelines are considered valid if for every step, the accumulated provide information of all previous steps satisfies the require constraints of the next step.

### Repair Units (Nice To Have but maybe to much)

Before entering the core conformal pipeline, input meshes are passed through an explicit preprocessing stage. This stage is responsible for turning “real-world” polygon data (often noisy, inconsistent, or non‑manifold) into a mesh that satisfies the structural requirements of the subsequent units

ConformalLab++ provides a small set of repair units that can be combined as needed:

+ removal of (almost) degenerate triangles (needles, caps),

+ stitching of compatible boundary cycles to close small gaps,

+ enforcing a consistent face orientation where possible.

These units are conceptually similar to geometric repair routines in modern polygon mesh processing toolkits

We distinguish between two typical modes of operation:

+ Soft cleaning: minimally invasive repairs intended for visualization and quick experiments. Soft cleaning tries to improve mesh quality without significantly altering topology or removing components.

+ Hard cleaning: more aggressive repairs intended for numerically robust experiments. Hard cleaning may merge vertices, remove tiny components, and modify local topology to enforce manifoldness and consistent orientation when possible.

## More internal representations (Nice To Have but maybe to much)
ConformalLab++ distinguishes between internal representation spaces that experiments may move between:

+ UniversalMesh: a halfedge‑based surface mesh representation used for most combinatorial and conformal algorithms.

+ PointCloud: an unstructured set of sample points, optionally with normals and additional attributes, used for sampling, resampling, and certain reconstruction tasks.

+ ImplicitField: a scalar field $f: \mathbf{R}^n \rightarrow \mathbf{R}$
represented on a grid or as a procedural function, used for iso‑surface extraction and robust shape transformations.

Each space has its own natural algorithms, and dedicated conversion units allow pipelines to move between these representations when needed.

### Conversion units

Typical conversion units include:

+ mesh_to_pointcloud (sampling vertices and surfaces of a UniversalMesh into a PointCloud),

+ pointcloud_to_mesh (surface reconstruction from point samples),

+ mesh_to_implicit (rasterizing a UniversalMesh into a signed distance or occupancy field),

+ implicit_to_mesh (iso‑surface extraction from an ImplicitField).

These units are modeled as regular processing units in the pipeline but change the underlying representation space instead of just transforming a mesh

## Attribute behaviour under topology changes (Nice To Have but maybe to much)

ConformalLab++ treats attributes as first-class data attached to mesh entities (vertices, edges, faces, halfedges). When topology changes, attributes are updated according to simple, explicit rules:

+ Vertex splits / edge splits: attributes on newly created vertices or edges are initialized by interpolation of the incident elements (e.g. linear interpolation of scalar fields along an edge).

+ Edge collapse: attributes on the surviving vertex are computed from the incident vertices, typically by a convex combination or area‑weighted average for scalar quantities.

+ Face operations (flip, subdivision): face attributes are either propagated (for categorical data) or interpolated (for scalar data) to new faces.

By default, ConformalLab++ uses linear interpolation for scalar attributes and nearest‑neighbour propagation for discrete or categorical attributes; units may override these policies where necessary