Abstract
Geometric transformations enable to represent spatial objects in different ways dependent of the kind of transformation. The methods of representation had not been combined with the idea of transformation at the beginning of their development. An important step had been done in the intellectual history of perspective, by bringing together the mathematical concept of projections and, further on, transformations with the representational concept of perspective according to seeing and perceiving. The step to projective geometry gave the possibility to apply the perspective transformation on objects in space and to receive again spatial objects by the transformation. The consequence had been a systematically theoretical work out of relief perspective as spatial transformation, which started as theatre stage design. This comprehension enables applications in architectural design processes. The fruitful interlacing of practice in art and architecture with mathematical theory will be reflected and applied in architectural design as spatial transformation considering perception.
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