Interactive Ray Tracing of Arbitrary Implicit Functions

We present a practical and efficient algorithm for interactively ray tracing arbitrary implicit surfaces. We use interval arithmetic both for reliable numerical computation and guaranteed detection of topological features. In conjunction with ray tracing, this allows for rendering literally any implicit surface simply from its definition. Interactive ray tracing facilitates flexible shading and visualization techniques, and allows dynamic rendering of higher-dimensional surfaces. Our method requires neither special hardware, nor pre- processing or storage of any data structure. Efficiency is achieved through SIMD optimization of both the interval arithmetic compu- tation and coherent ray traversal algorithm, delivering interactive results even for complex implicit functions.

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