Monocular 3D lane detection is a fundamental task in autonomous driving. Although sparse-point methods lower computational load and maintain high accuracy in complex lane geometries, current methods fail to fully leverage the geometric structure of lanes in both lane geometry representations and model design. In lane geometry representations, we present a theoretical analysis alongside experimental validation to verify that current sparse lane representation methods contain inherent flaws, resulting in potential errors of up to 20 meters, which raise significant safety concerns for driving. To address this issue, we propose a novel patching strategy to completely represent the full lane structure. To enable existing models to match this strategy, we introduce the EndPoint head (EP-head), which adds a patching distance to endpoints. The EP-head enables the model to predict more complete lane representations even with fewer preset points, effectively addressing existing limitations and paving the way for models that are faster and require fewer parameters in the future. In model design, to enhance the model's perception of lane structures, we propose the PointLane attention (PL-attention), which incorporates prior geometric knowledge into the attention mechanism. Extensive experiments demonstrate the effectiveness of the proposed methods on various state-of-the-art models. For instance, our methods enhance Persformer by 4.4 points, Anchor3DLane by 3.2 points, and LATR by 2.8 points on the overall F1-score. The code will be released upon publication.