Automatic Creation of Boundary-Representation Models from Single Line Drawings

Test Drawings

These test drawings can be found in electronic form in other places in more convenient formats. For example, many of them can be downloaded as a single zip file here.

Users are warned that:
I may add extra drawings without warning, as and when I need them;
I may correct errors in drawings without warning, as and when I find them;
I may resize drawings (usually making tiny drawings larger and huge drawings smaller) as and when I choose - the topology, edge angles and edge length ratios will remain the same, but the vertex coordinates will change;
I may change the pictorial drawings (for example by adding or removing whitespace border around the object) as and when I choose - the vertex/edge datasets are the "originals", and the .gif files which illustrate them are "derived works".

Trihedral Genus Zero Polyhedra

Trihedral Junction Catalogue

These drawings illustrate all possible trihedral junction labels (the labelled versions can be found here).

Yccc001 (natural line drawing only)
Yddd004 (natural line drawing only)
Wcdc002 (natural line drawing only)
Wdcd003 (natural line drawing only)
Lab002 (natural line drawing only)
Lac002 (natural line drawing only)
Lbd003 (natural line drawing only)
Lcb002 (natural line drawing only)
Lda003 (natural line drawing only)

Single Cubes

Various drawings which should ideally be interpreted as cubes.

Cube000 (natural line drawing only)
Cube100 (natural line drawing only)
Cube200 (natural line drawing only)
Cube300 (natural line drawing only)
Cube400 (natural line drawing only)
Cube500 (natural line drawing only)
Cube501 (natural line drawing and wireframe)
Cube600 (natural line drawing only)

Not Cubes

Various sketches, topologically equivalent to cubes, which should not be interpreted as cubes.

Bar100 (natural line drawing only)
Packet100 (natural line drawing only)
Packet200 (natural line drawing only)
Podium100 (natural line drawing only)
Wedge100 (natural line drawing only)
Crystal100 (natural line drawing only)

Axis-Aligned Extrusions

Beams and channels are standard engineering components. The remaining drawings are inspired by letters (e.g. the L-, T- and X-blocks) or are extrapolations of these ideas.

The C-Block illustrates the point that drawings of extrusions can include lines both ends of which are occluding T-junctions.
CBlock100 (natural line drawing only)

Right Extrusions of Non-axis-aligned End-caps

Prisms are common geometric objects.

Prism3 (natural line drawing only)
Prism6 (natural line drawing only)
Prism610 (natural line drawing only)
Prism620 (natural line drawing only)

The following four drawings can cause problems if the merit for rotational symmetry is too high: they are clearly not intended to be regular pentagonal prisms.
House000 (natural line drawing only)
House100 (natural line drawing only)
House200 (natural line drawing only)
Bureau100 (natural line drawing only)

Figure~\diag{VBLOCK100} is a simplification of Figure~\diag{EG-P2-19}; Notch100 takes the idea further.
VBlock100 (natural line drawing only)
Notch100 (natural line drawing only)
Notch200 (natural line drawing only)
TwoConcave (natural line drawing only)

This figure was inspired by the Anthracene molecule.
Anth100 (natural line drawing and wireframe)

Axis-Aligned Non-Extrusions

The Z-block, Figure~\diag{ZBLOCK100} appears in many previous investigations as being the simplest normalon with no other "clues": it is not an extrusion and has no axis of mirror symmetry. Other figures were inspired by other letters of the alphabet. Figure YCubes200 illustrates Kanatani's suggestion for labelling non-trihedral vertices. Note that the proper interpretation of Figure 4h-Th100 is non-trihedral and a geometrically-accurate interpretation of Figure~\diag{DENTS100} would contain degenerate vertices.

Figures Cupboard100 and Cupboard200 show that hidden topology can sometimes be at the front, not the back, of the object.
Cupboard100 (natural line drawing only)
Cupboard200 (natural line drawing only)

Figure LPlate100 illustrates a particular uncommon trihedral junction label pair.
LPlate100 (natural line drawing only)

Figure Plug210 illustrates that disconnected subgraphs can sometimes be part of the main block of an object and do not necessarily correspond to features.
Plug200 (natural line drawing only)
Plug210 (natural line drawing only)
TwoCubes100 (natural line drawing only)
Table220 (natural line drawing and wireframe)

Semi-Axis-Aligned with Mirror Plane

Grimstead's bracket (Figures~\diag{GRIM100} to~\diag{GRIM300}) was the figure chosen to demonstrate the capabilities of his system. The poorly-drawn Angle bracket (Figure~\diag{ANGLE300}) appears in [Sugihara] and other references to illustrate a common drawing error.

Grim100 (natural line drawing only)
Grim200 (natural line drawing only)
Grim300 (natural line drawing only)
SBracket100 (natural line drawing only)
Cut100 (natural line drawing only)
Angle100 (natural line drawing only)
Angle200 (natural line drawing only)
Angle300 (natural line drawing only)

Figure ABlock101 is a problem drawing: should it be mirror-symmetric or semi-axis-aligned with one non-axis-aligned face?
ABlock101 (natural line drawing only)
ABlock102 (natural line drawing only)

Architecture can often be approximated by semi-axis-aligned drawings with mirror planes.

HouseGarage100 (natural line drawing only)
HouseGarage200 (natural line drawing only)
Porch100 (natural line drawing only)
Porch200 (natural line drawing only)
Terrace200 (natural line drawing only)
Chimney100 (natural line drawing only)
TwoCubes200 (natural line drawing only)
Table300 (natural line drawing only)
Table301 (natural line drawing only)

Semi-Axis-Aligned without Mirror Plane

Semi-axis-aligned drawings without mirror planes are surprisingly uncommon.

LBlockPlus100 (natural line drawing only)
TruncPrism3 (natural line drawing only)
TruncPrism4 (natural line drawing only)
AnglePlus100 (natural line drawing only)

Regular and Semi-Regular

Although best handled as special cases, drawings of Platonic and Archimedean solids also make useful test cases for topological reconstruction using symmetry.

The last two figures show two views of one of the semi-regular convex solids (all faces are regular pentagons or squares, but not all vertices are interchangeable); there are several others (see Cromwell).
Semireg5544 (natural line drawing only)
Semireg55554 (natural line drawing only)

Right Frusta (by definition, not axis-aligned)

Inaccurate versions of Frust310 appear in several references, usually to illustrate the point that strictly mathematical approaches are intolerant of freehand drawing errors. Frust610 is a useful illustration of which edges can, and which edges cannot, be parallel.

Frust310 (natural line drawing only)
Frust320 (natural line drawing only)
Frust330 (natural line drawing only)
Frust410 (natural line drawing only)
Frust610 (natural line drawing only)
FrustU100 (natural line drawing only)

Other Trihedral

Wedge300 (natural line drawing only)
Chair600 (natural line drawing only)

Impossible Objects and Invalid Drawings

The Square contravenes either the general viewpoint or the most informative viewpoint assumptions.
Square (natural line drawing only)

The impossible objects, Penrose's frustum (Figure~\diag{PYRAMID333}), Sugihara's Box (Sugihara), Escher's Tower (EscherTower), Huffman's Combs (HuffComb000) and Cowan's Ring (Cowan000), are a reminder that not every valid topology can be realised geometrically.

Pyramid333 (natural line drawing only)
Sugihara (natural line drawing only)
EscherTower (natural line drawing only)
HuffComb000 (natural line drawing only)
Cowan000 (natural line drawing only)

Then again, some unexpected topologies can be realised geometrically. See Kokichi Sugihara's Web Site for instructions on how to build your own Escher Tower.

The degenerate objects illustrate why certain junction labels should not be included in the tetrahedral catalogue.
Mabcd000 (natural line drawing only)
Mdcab000 (natural line drawing only)
Kbdca000 (natural line drawing only)
Kbdca100 (natural line drawing only)
Kdabc000 (natural line drawing only)
Kdabc100 (natural line drawing only)

Non-Trihedral Genus Zero Polyhedra

Extended Trihedral

Figures~\diag{TBDA100}--\diag{YCUBES100} illustrate the entire extended trihedral junction catalogue.

Tbda100 (natural line drawing only)
Tbda200 (natural line drawing only)
Tbdc100 (natural line drawing only)
Tdab100 (natural line drawing only)
Tdab200 (natural line drawing only)
Tdac100 (natural line drawing only)
Tdac101 (natural line drawing and wireframe)

Xcbda100 (natural line drawing only)
4h-YCubes100 (natural line drawing only)

The trefoil, adapted from Cromwell, tests line labelling and topological reconstruction more seriously.
Trefoil100 (natural line drawing only)
LFrame500 (natural line drawing only)
FrontKBlock (natural line drawing only)

Non-Trihedral Pyramids

These drawings illustrate the view that all-convex pyramid vertices are commonly found in engineering objects, but single-concave pyramid vertices (Figures~\diag{PYRAMID450}--\diag{PYRAMID650} are not. Pyramid630 is an interesting optical illusion: the central vertex appears concave (compare with Figure~\diag{DENT100}), but the best geometric realisation is as an all-convex pyramid which is shallower at the top than the bottom.

Pyramid400 (natural line drawing only)
Pyramid430 (natural line drawing only)
Pyramid450 (natural line drawing only)
Pyramid500 (natural line drawing only)
Pyramid550 (natural line drawing only)
Pyramid600 (natural line drawing only)
Pyramid610 (natural line drawing only)
Pyramid630 (natural line drawing only)
Pyramid650 (natural line drawing only)

Plat20Dome (natural line drawing only)
Plat20DomeA (natural line drawing only)

Tetrahedral Junction Catalogue

These drawings illustrate the tetrahedral junction catalogue: see Appendix~\ref{4JCATDRAWINGS} for context. Their inclusion ensures that the implementation of each possible tetrahedral junction label is tested.

K-Vertex Objects

General Non-trihedral Objects

Figures~\diag{CUBEDOWN540}--\diag{CUBEUP500} illustrate another unsolved problem with line labelling, that of incorporating geometric information. Although architecture usually remains semi-axis-aligned and usually retains its mirror plane, non-trihedral vertices are common. Other drawings in this section illustrate non-trihedral vertices in engineering contexts (not all of the drawings in the previous section could be considered "common engineering objects") or are variants of those in the previous sections.

Objects with Through Holes

Through Holes Without Hole Loops

These drawings test object validation: in applying Euler's formula, it cannot be assumed that an object with no hole loops has no through holes. The Hannoid was taken from Sommerville et al. The modified Hannoid which follows it is interesting in that three identical parallelograms in the middle of the drawing signify entirely different things. Figures~\diag{SUGIHARA990}--\diag{SUGIHARA992} illustrate another problem with line labelling (what object do they represent?); one interpretation is the object used by Sugihara to illustrate a polyhedron with no first-order resolvable representation.

UUBlock100 (natural line drawing only)
UUBlock200 (natural line drawing only)
UUBlock300 (natural line drawing only)
LBlockHole200 (natural line drawing only)
LBlockHole201 (natural line drawing only)
Hannoid000 (natural line drawing only)
Hannoid100 (natural line drawing only)
Sugihara990 (natural line drawing only)
Sugihara991 (natural line drawing only)
Sugihara992 (natural line drawing only)

Axis-Aligned with Hole Loops

Distinguishing holes from bosses is usually straightforward (Figures Switch100 and Switch200 are counterexamples). Distinguishing holes from pockets is not (e.g. Figure~\diag{OXBLOCK300}). Identifying where a hole stops can also present problems when the face in which the hole terminates is not visible, as in Figures~\diag{MAZE111}--\diag{MAZE121}. Figure~\diag{WANGFRAME} shows an object more easily reconstructed by CSG methods [Wang] than B-rep.

Non-Axis-Aligned with Hole Loops

The method for distinguishing holes/pockets from bosses was derived for the axis-aligned case. These drawings test whether it works for non-axis-aligned drawings.

Chimney300 (natural line drawing only)
Balcony100 (natural line drawing only)
Prism3Hole100 (natural line drawing only)
Prism3Hole200 (natural line drawing only)
WedgeHole100 (natural line drawing only)

Extended K-Vertices

See [this paper] for a more detailed explanation of the problem posed by extended K-Vertices.

Some basic extended K-Vertex configurations

Multiple Polyhedra

RIBALD assumes that a drawing shows a single polyhedron.

ThreeCubes (natural line drawing only)

Figures based on Collections

Figures based on Yankee

As isometric projection can produce coincidences which break the "general viewpoint" rule, the viewpoints of most of these drawings have been changed slightly. Some drawings which originally included curves have been included: cylindrical through holes were either omitted from the object or converted to square or octagonal through holes, and corner blends were either omitted from the object or converted to octagonal corners. Where such simple adjustments were not available, the drawing was omitted. Some drawings have been duplicated, either in well-drawn and poorly-drawn versions, or (in the case of Figure~\diag{EG-FIG2-4S}) to add a plane of mirror symmetry.

EG-Fig6-3 (natural line drawing only)

Figures based on Pickup and Parker (Vol 1 and Vol 2)

As isometric projection can produce coincidences which break the "general viewpoint" rule, the viewpoints of most of these drawings have been changed slightly. Drawings which originally included curves have been omitted.

Figures from an Extrusion Catalogue

These extrusions appear in a catalogue of standard parts. Figure~\diag{CAPALEX-ROUNDBAR} illustrates one way in which RIBALD could process "curved" objects: although neither elegant nor ergonomic, it works.

Figures from Other Sources

Figures LS652 to LS660 are test drawings from Lipson and Shpitalni, included to provide a comparison between their methods and RIBALD's.
LS652 (natural line drawing only)
LS658 (natural line drawing only)
LS659a (natural line drawing only)
LS659b (natural line drawing only)
LS660 (natural line drawing only)

The next batch of figures were inspired by Meeran and Taib, whose interest is feature detection.
MeeranTaib894a (natural line drawing only)
MeeranTaib894b (natural line drawing only)
MeeranTaib894c (natural line drawing only)
MeeranTaib896 (natural line drawing only)
MeeranTaib901a (natural line drawing only)
MeeranTaib901b (natural line drawing only)

Figure Shirai2 comes from Shirai; the simplification in Figure Shirai looks more like an engineering component, but still includes a pentahedral (extended tetrahedral) vertex with two concave edges.
Shirai (natural line drawing only)
Shirai2 (natural line drawing only)

This figure is taken from Takahashi. The topological mirror symmetry is obvious to a human, but no algorithm we know of can single it out from all the other possibilities!