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Introduced 160 years ago as an attempt to generalize complex numbers to higher dimensions, quaternions are now recognized as one of the most important concepts in modern computer graphics. They offer a powerful way to represent rotations and compared to rotation matrices they use less memory, compose faster, and are naturally suited for efficient interpolation of rotations. Despite this, many practitioners have avoided quaternions because of the mathematics used to understand them, hoping that some day a more intuitive description will be available.The wait is over. Andrew Hanson's new boo

Quaternions. --- Algebra, Universal --- Algebraic fields --- Curves --- Surfaces --- Numbers, Complex --- Vector analysis --- Quaternions --- 681.3*I35 --- 681.3*I35 Computational geometry and object modeling (Computer graphics) --- Computational geometry and object modeling (Computer graphics) --- Computer graphics.

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Tax benefits to owner-occupied housing provide incentives for housing consumption, offsetting weaker disincentives of the property tax. These benefits also help counter the penalty federal taxes impose on households who work in productive high-wage areas, but reinforce incentives to consume local amenities. We simulate the effects of these benefits in a parameterized model, and determine the consequences of various tax reforms. Reductions in housing tax benefits generally reduce inefficiency in consumption, but increase inefficiency in location decisions, unless they are accompanied by tax-rate reductions. The most efficient policy would eliminate most tax benefits to housing and index taxes to local wage levels.

Zonder onderwerpscode: economie

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