We develop algorithms for color-weak compensation and color-weak simulation based on Riemannian geometry models of color spaces. The objective function introduced measures the match of color discrimination thresholds of average normal observers and a color-weak observer. The developed matching process makes use of local affine maps between color spaces of color-normal and color-weak observers. The method can be used to generate displays of images that provide color-normal and color-weak observers with a similar color difference experience. It can also be used to simulate the perception of a color-weak observer for color-normal observers. We also introduce a new database of measurements of color discrimination threshold data for color-normal and color-weak observers obtained at different lightness levels in CIELUV space. The compensation methods include compensations of chromaticity using local affine maps between chromaticity planes of color-normal and color-weak observers, and one-dimensional (1D) compensation on lightness. We describe how to determine correspondences between the origins of local coordinates in color spaces of color-normal and color-weak observers using a neighborhood expansion method. After matching the origins of the two coordinate systems, a local affine map is estimated by solving a nonlinear equation, or singular-value-decomposition (SVD). We apply the methods to natural images and evaluate their performance using the semantic differential (SD) method.