For years I’ve wished to learn enough hyperbolic geometry to write a simple ray-tracer. Recently a post on comp.graphics.algorithms advised me to look up Euclidean and Non-Euclidean Geometry by Patrick J. Ryan; I was pleased to find that its subtitle is An Analytic Approach. Indeed it gives most of what I was looking for; though it relies so much on cross products that extending from two dimensions to three may be difficult.
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