QUANTITATIVE MEASURES
Using values from Tissot (see Box 5.A) on all conformal projections,a = b every where on the projection. When a=b, the value of 2โอม is 0°.Hence there is no angular deformation at points on con- formal projections. Because the values of a and b vary from place to place, however, the product of ab will alsovary from place toplace. Consequently, all conformal transformations enlarge or reduce areas relative to one another. The product ab at various points provides an index of the degree of areal change.On equal-area projections, the scale relation- ships at each point are such that the product of ab always equals 1.0. Any difference between the values of a and b produces a value of 2โอม greater than 0° Consequently, all equal-area projections deform angles. The value of 2โอม at various points provides an index of the degree of angular distortion. On projections that are neither conformal nor equalarea, a will not equal b. Nor will the product the values of Sand 2โอม will vary from place to place and serve as quantitative measures of the distor tion
QUANTITATIVE MEASURES Using values from Tissot (see Box 5.A) on all conformal projections,a = b every where on the projection. When a=b, the value of 2โอม is 0°.Hence there is no angular deformation at points on con- formal projections. Because the values of a and b vary from place to place, however, the product of ab will alsovary from place toplace. Consequently, all conformal transformations enlarge or reduce areas relative to one another. The product ab at various points provides an index of the degree of areal change.On equal-area projections, the scale relation- ships at each point are such that the product of ab always equals 1.0. Any difference between the values of a and b produces a value of 2โอม greater than 0° Consequently, all equal-area projections deform angles. The value of 2โอม at various points provides an index of the degree of angular distortion. On projections that are neither conformal nor equalarea, a will not equal b. Nor will the product the values of Sand 2โอม will vary from place to place and serve as quantitative measures of the distor tion
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