Presentation on theme: "Animating Impossible Objects Peter Kovesi and Chih Khoh School of Computer Science & Software Engineering The University of Western Australia."— Presentation transcript:
Animating Impossible Objects Peter Kovesi and Chih Khoh School of Computer Science & Software Engineering The University of Western Australia
An impossible figure is a two-dimensional image that is interpreted to give the impression of some three-dimensional object that cannot exist.
image3D model vision graphics
3D model image vision graphics ! ?
Uccello: The Battle of San Romano ~1430
Uccello: The Hunt ~1460
Uccello Drawing of a Chalice
False Perspective, William Hogarth (1753)
Giovanni Battista Piranesi 14 th Prison (1760)
Swedish artist Oscar Reutesvard was the first to intentionally construct impossible figures. He devised this version of the impossible tri-bar in 1934
In 1958 Penrose independently devised the impossible tri-bar and published a paper (with his dad) in the British Journal of Psychology. Correspondence between Penrose and Escher resulted in this image Waterfall (1961)
Ascending Descending (1960) Penrose also devised the impossible staircase
Why are Objects Impossible? (Huffman: Impossible Objects as Nonsense Sentences, 1971) Line Labeling Inconsistency +Convex edge. -Concave edge. ^Occluding edge (surface to the right). Apparent contour (surface to the right). ^ ^ Shigeo Fukuda
But some impossible objects can be labeled consistently…
The Aspect Graph (Koenderink and van Doorn 1979) Nodes:Generic views, or aspects of an object. Edges:Possible transitions between aspects. Aspect graph of a tetrahedron
Aspect Graph of a Cube An impossible object can result from the simultaneous presentation of two distant aspects of an object.
“An impossible figure is a two-dimensional image that is interpreted to give the impression of some three-dimensional object that cannot exist.” But some impossible 3D objects are possible…
Impossible triangle by Mathieu Hamaekers
A 3D model must be handcrafted to suit the viewpoint. A computer model has an advantage in that it can be continuously adjusted to suit the viewpoint …
Constructing Impossible Figures via Complementary Halves An impossible rectangle and its two halves, each of which are globally consistent
One complementary half can be obtained from the other via reflections across two orthogonal axes
An impossible rectangle can also be created by reversing the visibility of the faces on one half of a possible rectangle
The Necker Cube and its two interpretations
Donald Simanek’s Ambiguous Ring
The Impossible Stall: The basis of Escher’s Belvedere
Model of Belvedere by Shigeo Fukuda
Model of Belvedere by Shigeo Fukuda
Model of Waterfall by Shigeo Fukuda
The Crazy Crate
Mathieu Hamaekers and his model of an impossible crate
Rotating the Impossible Rectangle
Animation Requires Continuous Modification of the 3D Model Failure to adjust thickness during rotation produces halves that cannot be joined Note how the bars of this crazy crate must be non-square to allow joining
1.Construct 3D model of one half of the object (origin at the centre point of join). 2.Orient it to the desired view. 3.Project into the image plane (orthographic projection). 4.Calculate projected widths of surfaces to be joined. 5.Rescale widths of corresponding surfaces on the 3D model to allow joining in 2D. 6.Construct second half by negating X and Y coordinates (Z values unchanged). 7.Add lines to the 2D image to ‘fix’ the join as necessary. Algorithm
Challenges… Model by Shigeo Fukuda Non-even symmetry Line labeling inconsistency Impossible stereo/autostereograms. Impossible shading/lighting. Impossible motion.
A computer model of Esher’s “High Low” by Sascha Ledinsky rendered in POV-ray.