Abstract. If the product designer wants to assure that a non-ideal part (either manufactured or simulated) that meets the defined tolerances will fulfill its function, the variant part has to be positioned in the context of its assembly. After this positioning step, further visualization or analysis methods can be accomplished. In this paper, we describe a method to place measured or simulated parts in the context of the assembly in an ideal way concerning defined objectives. The needed input of our method is an ideal assembly that can include tolerances and one or more non-ideal parts of that assembly. Then a position for each non-ideal part is calculated by heuristic optimization, resulting in an assembly where the ideal parts are replaced by the non-ideal parts. Commonly used registration methods minimize the distance between nominal and non-ideal parts, but do not take into account the environment of the part; known relative positioning methods use simplified geometry models so far. In this paper, we present a new optimization-based approach to position three-dimensional non-ideal parts and show experimental results of our implementation.