Restitution and Interpretation of Spatial Representations
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Restitution and interpretation of spatial representations

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.


Case of restitution polyhedron of melencolia i of a d rer 1514

Case of restitution :polyhedron of « Melencolia I »of A. Dürer(1514)


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.


Coherence of hidden lines comparison with a sketch of d rer

Coherence of hidden lines :Comparison with a sketch of Dürer


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


Use of duality for correction a complementary tool

Use of duality for correctiona complementary tool


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°


3d restitution using photomodeler1

3D RestitutionUsing « Photomodeler »


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…


Restitution and interpretation of spatial representations

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