Improved moving least squares algorithm for directed projecting onto point clouds

Directed projection is a key issue in many point-based techniques in geometric modeling, computer graphics, and computer vision. This paper proposes a new point-based directed projection method in the frame of moving least squares (MLS) projection where the reference plane is determined by approximating its normal using weighting least squares method, and the weighting value, on every neighboring points is determined according to the distance from the point to the projection ray. At every optimal step, the normal is calculated from updated neighborhood to relocate the reference plane, and check the variation in energy. The resulting solution is obtained with the local minima of the energy. Comparing with the existing directed projection algorithm, the proposed method is more robust and efficient, especially for the surfaces with complex profiles. To demonstrate the valid of the proposed approach and its application in part manufacturing, several numerical experiments have been presented and the results show that it is promising.

► A directed projection method is proposed based on moving least squares.
► A new method is proposed to calculate the closest intersection of point cloud and ray.
► The quality of fit of the reference plane to point cloud is measured by energy.
► It is a rapid, robust and inexpensive in calculation.