The point cloud is an unorganized set of points with 3D coordinates (x, y, z) which represents a real object. These point clouds are acquired by the technology called 3D scanning. This scanning technique can be done by various methods, such as LIDAR (Light Detection And Ranging) or by utilizing recently developed 3D scanners. Point clouds can be therefore used in various applications, such as mechanical or reverse engineering, rapid prototyping, biology, nuclear physics or virtual reality. Therefore in this doctoral Ph.D. thesis, I focus on feature detection and visualization in a point cloud. These features represent parts of the object that can be described by the well--known mathematical model (lines, planes, helices etc.). The points on the sharp edges are especialy problematic for commonly used methods. Therefore, I focus on detection of these problematic points. This doctoral Ph.D. thesis presents a new algorithm for precise detection of these problematic points. Visualization of these points is done by a modified curve fitting algoritm with a new weight function that leads to better results. Each of the proposed methods were tested on real data sets and compared with contemporary published methods.