We present two distance field representations which can preserve sharp features in original geometric models: the offset distance field (ODF) and the unified distance field (UDF). The ODF is sampled on a special curvilinear grid named an offset grid. The sample points of the ODF are not on a regular grid and they can float in the cells of a regular base grid. The ODF can naturally adapt to curvature variations in the original mesh and can preserve sharp features. We describe an energy minimization approach to convert geometric models to ODFs. The UDF integrates multiple distance field representations into one data structure. By adaptively using different representations for different parts of a shape, the UDF can provide high fidelity surface representation with compact storage and fast rendering speed.