A 3-D image-to-device gamut mapping algorithm (I-D GMA) is an ideal way to map display image to the inside of printer gamut. A quick decision whether or not each pixel is located inside of the device gamut is necessary to execute a 3-D I-D GMA. We propose a new gamut boundary descriptor (GBD) for comparing the gamut between image and device by the discrete polar angle (Δθ, Δφ). The gamut shell is described as the simple radial distances, called an r-image. We discuss the location of optimum focal points as mapping centers in an r-image for 3-D I-D GMA. The performance of a 3-D I-D GMA using an r-image is evaluated in the two cases of single and multiple focal points. To maintain the continuous gradation of an image after mapping, the device gamut shell should have a smooth and a precise surface. The printer gamut shell is simply shaped like a polygon made of a triangular mesh pattern, but shaped to have a smoother surface by introducing Overhauser spline functions. Psychophysical experiments were carried out to assess the color appearance matching between the original CRT image and the printed hard copies after mapping. The performance of the 3-D I-D GMA is compared with that of a conventional device-to-device gamut mapping algorithm (D-D GMA). We claim that the 3-D I-D GMA using multiple focal points and a spline GBD achieves the best mapping results for the wide gamut images.