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To improve the coding performance of depth maps, 3D-HEVC includes several new depth intra coding tools at the expense of increased complexity due to a flexible quadtree Coding Unit/Prediction Unit (CU/PU) partitioning structure and a huge number of intra mode candidates. Compared to natural images, depth maps contain large plain regions surrounded by sharp edges at the object boundaries. Our observation finds that the features proposed in the literature either speed up the CU/PU size decision or intra mode decision and they are also difficult to make proper predictions for CUs/PUs with the multi-directional edges in depth maps. In this work, we reveal that the CUs with multi-directional edges are highly correlated with the distribution of corner points (CPs) in the depth map. CP is proposed as a good feature that can guide to split the CUs with multi-directional edges into smaller units until only single directional edge remains. This smaller unit can then be well predicted by the conventional intra mode. Besides, a fast intra mode decision is also proposed for non-CP PUs, which prunes the conventional HEVC intra modes, skips the depth modeling mode decision, and early determines segment-wise depth coding. Furthermore, a two-step adaptive corner point selection technique is designed to make the proposed algorithm adaptive to frame content and quantization parameters, with the capability of providing the flexible tradeoff between the synthesized view quality and complexity. Simulation results show that the proposed algorithm can provide about 66% time reduction of the 3D-HEVC intra encoder without incurring noticeable performance degradation for synthesized views and it also outperforms the previous state-of-the-art algorithms in term of time reduction and $\Delta $ BDBR. [ABSTRACT FROM AUTHOR]