The goal of advanced geometric algorithms is to handle core operations
robustly and accurately.
In computer-aided-design (CAD), this means to
store and manipulate surfaces within a high tolerance. The goal is
to provide gap-free and efficient representations without using redundant
elements, and efficiently execute standard geometric operations such as
surface trimming, healing, compression,
repair, and the core Boolean operations of union, addition, and subtraction.
In computer-aided machining (CAM), this means to create clean,
robust, and accurate toolpaths for reliable, efficient and rapid machining,
to automatically determine cut/uncut regions for finishing, as well as detect
features for particular operations, and provide efficient work-in-progress
and verification models.
Many packages fail when the surfaces and shapes become complex. In
CAD, this can result in inefficient representations and corrupt surfaces.
In CAM, this can result in toolpaths that are broken, gouge the material, or
miss small but crucial details.
The requirement of strict tolerances adds additional complications.
Interfacial has built a core technology to address these issues. The cornerstones are several proprietary algorithmic advances:
- Geometrical Libraries: The development of
geometrical libraries to handle local, topologically complex events. These
include surface trimming, healing, compression, and determination of
interconnectivities and multiple junctions.
- Boolean Operations: The ability to perform exact Boolean operations,
including union, intersection, and subtraction of arbitrary surfaces.
- Watertight Offsets: The ability to generate exact watertight offsets
of surfaces, starting with either NURBS or triangulated surfaces
representations. These can be generated using
offsets of arbitrary shape, both convex and non-convex. Internal offseting
correctly produces internal voids and structures.
- Exact On-Surface Navigation: The ability to
exactly project an off-surface curve to its closest on-surface representation,
as well as the ability to perform on-surface navigation to determine closest
points and geodesics.
Advantages to this approach
These four technologies, in tandem, can be used to robustly solve a host of
outstanding CAD and CAM problems. These include:
- Surface Conversion, Repair, and Compression:
Using these geometrical libraries, conversion from NURBS into triangulated
data is clean and reliable, including input from IGES and Parasolid.
The modules provide automatic detection of corrupt or faulty input files,
with suggested corrections.
The modules can clean up surfaces, including stitching together gaps within a user-specified tolerance as well as compress unnecessarily large files.
- Surface Trimming and Sculpting:
Given a surface/body and off-surface trim curves, the geometrical
libraries can find the closest on-surface curves, and then produce an
on-surface body-fitted mesh: this provides the ability to sculpt surfaces
and resolve a host of issues that arise when inconsistent inputs from
multiple CAD packages.
- Surface Operations and Measurement:
The Boolean operations provide the ability to combine complex shapes in order
to build moulds, as well as carve figures and apply imprints.
In addition, the geometric libraries provide surface measurements on intricate
surfaces, including shortest paths between pairs of points and on-surface
ruling and mesh generation.
- Toolpaths for Machining: Because the offset surfaces are clean and watertight,
fast generation of guaranteed gouge-free toolpaths is straightforward, and include zcuts, planecuts,
radial and spiral cuts, and constant stepover.
- Uncut/Leftover and Automatic Finishing: For a given tool shape, orientation and tolerance, the Boolean
libraries allow exact reclassification and tesselation of the base input surface into
machinable and non-machinable regions. This is a fully three-dimensional re-triangulation
of the base into reachable and non-reachable regions, allowing automatic finishing paths
on restricted regions.
Accuracy, Robustness, and Efficiency
InterfacialTM modules are designed to produce highly accurate, robust solutions efficiently:
- Accuracy: All outputs are guaranteed to fall within a strict, user-defined
tolerance. For example, for machinable surfaces of size 10000 mm, Interfacial modules provide
toolpaths, gouge checking, and offset surfaces with an accuracy of .000001. Higher accuracy modules
are also available.
- Robustness: Rather than work top-down through a series of ad-hoc decisions,
Interfacial modules correctly analyze local surface interactions.
This means that the modules are guaranteed to finish with the correct, checkable and verifiable solution.
- Efficiency: Interfacial data structures are built to handle large, complex
input surfaces efficiently, using some proprietary pruning/elimination
techniques. For example, on
a standard single processor 2 GHz Pentium IV:
- Perform Boolean Operations:
- To subtract a 50,898 triangle surface
from a 76,0044 triangle surface, with over 20,064 intersecting triangles,
- Build Zcuts:
[Base Surface 175,000 triangles (22cm by 16cm by 3cm)]
- .5 radius ball tool, tolerance of .01, zcut interval=.05: generates 600 zcuts, 16 seconds
- .15 radius ball tool, tolerance of .001, zcut interval=.05: generates 600 zcuts, 28 seconds
- Build Clean Offset:
[Base Surface 175,000 triangles (22cm by 16cm by 3cm)]
- .5 radius ball tool, tolerance of .01: generates 231,442 triangles, 105 seconds
- .15 radius ball tool, tolerance of .001: generates 600,470 triangles, 193 seconds
Versatility and Portability
InterfacialTM modules are designed for maximum versatility and portability.
They are written as DLLs, callable through multiple platforms and environments. The suite of modules include:
- Automatic Buffering: The modules provide automatic buffering for very large data sets. Minimum memory requirement is less than 100K RAM.
- Integrability: Interfacial modules are written
as DLLs, callable through multiple platforms and environments. They have
compact, black-box calling sequences, and act as low-level engines designed
to be quickly put in place.
InterfacialTM modules are in daily use by tens of thousands of