Grasping has been a long-standing challenge in facilitating the final interface between a robot and the environment. As environments and tasks become complicated, the need to embed higher intelligence to infer from the surroundings and act on them has become necessary. Although most methods utilize techniques to estimate grasp pose by treating the problem via pure sampling-based approaches in the six-degree-of-freedom space or as a learning problem, they usually fail in real-life settings owing to poor generalization across domains. In addition, the time taken to generate the grasp plan and the lack of repeatability, owing to sampling inefficiency and the probabilistic nature of existing grasp planning approaches, severely limits their application in real-world tasks. This paper presents a lightweight analytical approach towards robotic grasp planning, particularly antipodal grasps, with little to no sampling in the six-degree-of-freedom space. The proposed grasp planning algorithm is formulated as an optimization problem towards estimating grasp points on the object surface instead of directly estimating the end-effector pose. To this extent, a soft-region-growing algorithm is presented for effective plane segmentation, even in the case of curved surfaces. An optimization-based quality metric is then used for the evaluation of grasp points to ensure indirect force closure. The proposed grasp framework is compared with the existing state-of-the-art grasp planning approach, Grasp pose detection (GPD), as a baseline over multiple simulated objects. The effectiveness of the proposed approach in comparison to GPD is also evaluated in a real-world setting using image and point-cloud data, with the planned grasps being executed using a ROBOTIQ gripper and UR5 manipulator.