As the last step of product manufacture, assembly process has significant effect on the performance and quality of product [1]. Assembly sequence planning is the basis to implement assembly activity. According to the assembly sequence of parts and components, specifying reasonable inspection, process operations, assembly fix and material are the foundation to obtain high efficiency for assembly and guarantee the assembly quality [2, 3]. As a powerful digital technology, virtual assembly is capable to validate the accessibility and evaluate the performance of assembly process in early assembly process design stage, e.g. ensuring the feasible assembly sequence by simulating the assembly process with collision detection, which contributes to avoid assembly interference due to mistake assembly process and shorten the period of assembly process design [4].

Interference matrix is an important information model for assembly sequence planning that working via relationship matrix. It represents the relative spatial position between parts which is the important basis to judge the feasibility for part assembly [5]. Normally, interference matrix indicates it is interference or not of each part moving out the whole assembly room along the positive / negative directions of three coordinate frame axes with the other parts. For interference matrix *A*D in direction D, it is element *A*D[i,j] stores the interference result of moving part *i* along direction *D* with part *j*, which including three cases, i.e. interference-free, contact, and hard-collision [6].

Identifying the interference elements values, normally, is adopting the classic triangle-based rigid objet collision detection method. The object part is moving step by step with specific step length, and the collision detection is performed for each position between object part and the opposite part to report is there any interference occurred. However, it is low efficient, particular for plenty of parts with complex geometry since the collision detections lead to heavy computation, huge-memory requirement, and spend long time. Besides, it is significant to accurately distinguish interference and contact for interference matrix establishing since contacts are common exist in mechanical part assembly like shaft-hole, panel align panel etc. Therefore, it enhances the compute difficult for collision detection algorithms and heavier compute load.

Actually, the establishment of interference matrix establishment is met that only checking it is interference or not for object part taking linear motion with opposite part. Therefore, it is hopeful to improve the computation efficiency by dimension-reduction in viewpoint of image-space where represents the swept volume of object part by the projection area of view volume for object part along moving direction. Besides, with the performance boosting of Graphic Processing Uniting (GPU), image-based collision detection methods gain excellent performance by utilizing the powerful parallel computation capability of GPU to seed up task calculation [7]. As the two of most classic ones, RECODE [8] and CULLIDE [9] employ the depth buffer, stencil buffer, occlusion query etc. in image space to perform collision detection computation. In this basis, according to the dimension reduction ideology, Zhou et al [10] proposed a fast collision detection method based on the Z-buffer, which good at the real-time collision report for first person roams in virtual scene by providing the spatial coordinate value of specific pixel to perform collision detection. To deal with the collision detection during kinematic simulation of mechanical system, Sun et al [11] developed a dual view and semi-transparent color overlap collision detection algorithm, which transforming the problem as panel pixel judgement by projection based dimension reduction, resulting to meet the real time requirement during virtual assembly simulation. With respect to the characteristic of stream computation for GPU, Liu et al [12] represented a collision detection that combine both model space and image space for the purpose that employing the parallel computation speed up of GPU without lose the real-time and accuracy of algorithm. Kim et al [13] developed the hybrid parallel continuous collision detection (HPCCD) to obtain significant improvement in efficiency by utilizing the computation capability of both GPU and many-CPU. These methods have indicated that image-based collision detection show extraordinary efficiency improvement by reducing the dimension of mathematical model for collision detection task. However, establishing the interference matrix for complex mechanical system by directly adopting the image-based collision detection algorithms still subject to heavy compute task and result to low efficiency.

To overcome this drawback, a geometry space and image space combined collision detection algorithm is developed with respect to the special requirement of collision detection for interference matrix element establishment. It identifies the obvious interference-free element by spatial boundary box based on conservatism in rough stage, and performs precise interference checking by a delicate algorithm with adopting Z-buffer and stencil buffer through OpenGL. Finally, it not only reaches a high compute efficiency but also capable to report interference and contact cases for assembly interference matrix establishment. The rest of part is arranged as follows: section 2 represent the rough stage of interference matrix calculation by boundary box; The complete image-based collision detection algorithm performed by OpenGL including both calculation principle and concrete algorithms are described in section 3; In section 4, examples are studied and discussed and concluded at last.