Table 4.6.1 lists expressions for a vector N, normal to a surface defined either explicitly by and equation of the form ; or implicitly, by an equation of the form , where is a real constant.
Surface defined explicitly
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Surface defined implicitly
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Table 4.6.1 Surface normals for surfaces defined explicitly and implicitly
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If the gradient is normal to the level surface defined implicitly by an equation of the form , then writing the equation for the explicitly given surface in the implicit form , leads to the surface normal