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Restitution and Interpretation of Spatial Representations A New Approach for Teaching RepresentationThierry Ciblac, Louis-Paul Untersteller, Pierre Macé  ARIAM - LAREAEcole Nationale Supérieure d’Architecture de Paris la Villette - France[tciblac, lpu, pmace]@paris-lavillette.archi.freCAADe 2006
restitution and interpretation of spatial representations
Restitution and Interpretation of Spatial Representations
  • Introduction
  • Case of restitution : polyhedron of « Melencolia I » of A. Dürer
  • Case of restitution when sketching : inclined skylight
  • Conclusion
architects and spatial representations
Architects and spatial representations
  • Precise drawers?
  • Check and evaluate 3D representations
  • From 2D to 3D :
    • mental reconstruction of 3D objects : from 2D images
    • 3D restitution : 3D model from photographs, sketches in perspective…
  • What knowledge?
theoretical tools for restitution
Theoretical tools for restitution

Use of geometrical properties, not only drawing knowhow

Properties :

  • Incidence properties in projective geometry
  • Parallelism, orthogonality properties in affine geometry
  • Metric properties in Euclidian geometry.
coherence of the 2d representation correction of the drawing
Coherence of the 2D representation :Correction of the drawing
  • Hypothesis : Plane faces
  • Tools : Incidence properties.

« 3 planes meet in one point »

=B’3

E’’

E’’

coherence of the 2d representation determination of hidden lines
Coherence of the 2D representation :Determination of hidden lines
  • Hypothesis : Plane faces

but no hypothesis of parallelism.

  • Tools : Incidence properties, auxiliary planes.
parallelism correction for parallel faces
Parallelism :Correction for parallel faces
  • Hypotheses : Plane faces,

parallelism of opposite faces.

magenta : parallelepiped

orange : triangles in parallel planes

  • Tools : incidence properties, vanishing points (parallelism).

pf1, pf1, pf3 : vanishing points of the direction of edges of a parallelepiped closed to the polyhedron

parallelism rebuilt polyhedron s projection
Parallelism :rebuilt polyhedron’s projection

Comparison with the sketch :

magenta : parallelepiped

orange : triangles in parallel planes

black : corrected sketch

symetry and orthogonality principal point principal distance
Symetry and Orthogonality :principal point, principal distance
  • New Hypothesis :
  • equilateral triangles (give two couples of orthogonal directions)
3d restitution using photomodeler
3D RestitutionUsing « Photomodeler »

Hypotheses :

The principal point and principal distance are known.

Symmetry of 120° according to a « vertical » axis.

Initial position rotation of 120° rotation of 240°

case of restitution when sketching inclined skylight inspired by the vitra museum of f ghery
Case of restitution when sketching :inclined skylightinspired by the Vitra museum of F. Ghery
conclusion
Conclusion
  • Powerful theoretical tools
  • Implementation (Grassman Cayley algebra…)
  • Research : sketch restitution (Gina Project…)
  • Teaching these tools to architects…
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