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The discrete Tchebichef transform (DTT) is a transform method based on discrete orthogonal Tchebichef polynomials, which have applications recently found in image analysis and compression. This letter introduces a new fast 4 4 forward DTT algorithm. The new algorithm requires only 32 multiplications and 66 additions, while the best-known method using two properties of the DTT requires 64 multiplications and 96 additions. The proposed method could be used as the base case for recursive computation of transform coefficients. Experimental results showing performance improvement over existing techniques are presented.

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Figure 1. The LineFORM actuated curve interface can transform between shapes for mobile interaction: a) curve, b) wristband, c) surface, d) phone.

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Shape changing interfaces give physical shapes to digital data so that users can feel and manipulate data with their hands and bodies. However, physical objects in our daily life not only have shape but also various material properties. In this paper, we propose an interaction technique to represent material properties using shape changing interfaces. Specifically, by integrating the multi-modal sensation techniques of haptics, our approach builds a perceptive model for the properties of deformable materials in response to direct manipulation.As a proof-of-concept prototype, we developed preliminary physics algorithms running on pin-based shape displays. The system can create computationally variable properties of deformable materials that are visually and physically perceivable. In our experiments, users identify three deformable material properties (flexibility, elasticity and viscosity) through direct touch interaction with the shape display and its dynamic movements. In this paper, we describe interaction techniques, our implementation, future applications and evaluation on how users differentiate between specific properties of our system. Our research shows that shape changing interfaces can go beyond simply displaying shape allowing for rich embodied interaction and perceptions of rendered materials with the hands and body.

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