text: The aim of tool path planning is to maximize the efficiency against some given precision criteria. In practice, scallop height should be kept constant to avoid unnecessary cutting, while the tool path should be smooth enough to maintain a high feed rate. However, iso-scallop and smoothness often conflict with each other. Existing methods smooth iso-scallop paths one-by-one, which make the final tool path far from being globally optimal. This paper proposes a new framework for tool path optimization. It views a family of iso-level curves of a scalar function defined over the surface as tool path so that desired tool path can be generated by finding the function that minimizes certain energy functional and different objectives can be considered simultaneously. We use the framework to plan globally optimal tool path with respect to iso-scallop and smoothness. The energy functionals for planning iso-scallop, smoothness, and optimal tool path are respectively derived, and the path topology is studied too. Experimental results are given to show effectiveness of the proposed methods.
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  @cite_2: This paper presents an analytical method for planning an efficient tool-path in machining free-form surfaces on 3-axis milling machines. This new approach uses a nonconstant offset of the previous tool-path, which guarantees the cutter moving in an unmachined area of the part surface and without redundant machining. The method comprises three steps : (1) the calculation of the tool-path interval, (2) the conversion from the path interval to the parametric interval, and (3) the synthesis of efficient tool-path planning.
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  @cite_4: This paper presents a novel approach for generating efficient tool paths in machining free-form surfaces. Concept of iso-phote is used to facilitate tool-path generation. An iso-phote is defined as a region on a surface where the normal vector does not differ by more than a prescribed angle from a fixed reference vector. The boundary curves of the iso-phote, called iso-inclination curves, are numerically generated and are served as the initial master tool paths. These iso-inclination curves are then projected to a 2D plane which is perpendicular to the fried reference vector. 2D curve offsetting of the projected iso-inclination curve is then performed. The resulted 2D offset curves are projected back to 3D surface to form final tool paths. The resulted tool paths can guarantee the satisfaction of machining tolerance requirements. A comparison study of this iso-phote based machining with the conventional iso-parametric machining and the iso-planar machining shows favorite result for the new approach.
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  @cite_23: A novel approach for the NC tool-path generation of free-form surfaces is presented. Traditionally, the distance between adjacent tool-paths in either the Euclidean space or in the parametric space is kept constant. Instead, in this work, the scallop-height is kept constant. This leads to a significant reduction in the size of the CL (cutter location) data accompanied by a reduction in the machining time. This work focuses on the zig-zag (meander) finishing using a ball-end milling cutter.
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  @cite_19: An algorithm for three-axis NC tool path generation on sculptured surfaces is presented. Non-constant parameter tool contact curves are defined on the part by intersecting parallel planes with the part model surface. Four essential elements of this algorithm are introduced: initial chordal approximation, true machining error calculation, direct gouge elimination, and non-constant parameter tool pass interval adjustment. A software implementation of this algorithm produces graphical output depicting the tool path superimposed over the part surface, and it outputs cutter location (CL) data for further post-processing. Several applications examples are presented to demonstrate the capabilities of the algorithm. The results of this technique are compared to those generated from a commercially available computer-aided manufacturing program, and indicate that equivalent accuracy is obtained with many fewer CL points.
  @cite_27: In free-form surface milling, cusps on a part surface need to be regulated. They should be small enough for precision purposes. On the other hand, we should maintain high enough cusps so as not to waste effort making unnecessary cuts. A widely accepted practice is to maintain a constant cusp height over the surface. This paper introduces a new approach to generating constant cusp height tool paths. First, we define a Riemannian manifold by assigning a new metric to a part surface without embedding. This new metric is constructed from the curvature tensors of a part and a tool surface, which we refer to as a cusp-metric. Then, we construct geodesic parallels on the new Riemannian manifold. We prove that a selection from such a family of geodesic parallels constitutes a ''rational'' approximation of accurate constant cusp height tool paths.
  @cite_16: Numerically controlled milling is the primary method for generating complex die surfaces. These complex surfaces are generated by a milling cutter which removes material as it traces out pre-specified tool paths. The accuracy of tool paths directly affects the accuracy of the manufactured surface. The geometry and spacing of the tool paths impact the scallop height and time of manufacturing respectively. In this paper we propose a new method for generating NC tool paths. This method gives the part programmer direct control over the scallop height of the manufactured surface. The method also provides options to the part programmer for generating a variety of tool paths based on practical metrics such as tool path length, tool path curvature and number of tool retractions.
  @cite_25: The continuation of a trend towards more user-friendly, interactive CADCAM systems, prompted the creation of a prototype software package called CISPA (Computer Interactive Surfaces Pre-APT). This system uses a menu-driven front end with graphical feedback to guide a user through curve and free form surface definition resulting in a mathematical model which may be used to generate NC machine CLSF. This front end was built upon the curve and surface complex taken from CAM-I's CASPA (Computer-Aided Sculptured Pre-APT). This complex is part of the execution phase of APT 4. Improvements were made in the definition and calculation of step size basing the input on geometric attributes such as chordal deviation and scallop height rather than on abstract algebraic quantities. Further additions include increased flexibility in milling surfaces, by roughing to depth.
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  @cite_33: Presented in the paper is a new approach to tool-path generation for sculptured surface machining. In the proposed C-space approach, the geometric data describing the design-surface, stock-surface and tool shape are transformed into C-space elements, and then, all the tool-path generation decisions are made in the configuration space (C-space). The C-space approach provides a number of distinctive features suitable for sculptured surface machining, including: 1) gouge-free tool-paths; 2) uncut handling; 3) balanced cutting-load; 4) smooth cutter movement; 5) collision-free tool-path.
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  @cite_0: Recently, a large amount of new research related to numerical control (NC) tool path generation has appeared in the literature. Unfortunately, finding information on a particular topic can be difficult. Not only does path generation span several disciplines, but the material tends to vary both in content and focus. In this paper, the literature is partitioned into categories and papers related to path generation classified according to the topics they cover. This should be useful to those looking for references on specific topics as well as those seeking an introduction to the literature as a whole.
  @cite_13: 
summary: Last decade has seen a great deal of literature on tool path planning for free-form surfaces, such as iso-parametric method @cite_25 @cite_12 @cite_1 , iso-planar method @cite_19 @cite_9 @cite_18 , iso-scallop method @cite_23 @cite_32 @cite_13 @cite_17 @cite_3 @cite_8 @cite_21 , iso-phote method @cite_4 and C-space method @cite_33 , to name a few. Surveys of much more work about tool path planning research can be found in @cite_0 @cite_30 . Since we aim at optimal tool paths with respect to iso-scallop and smoothness, we put special interest in the iso-scallop method, which means the height of the points at the scallop curves remains as high as a given value so that the tool path has no unnecessary cutting. Conventionally, constant scallop height is obtained by varying the offset magnitude along each path. A mathematical method for generating iso-scallop tool paths following such strategy was first proposed by @cite_23 . Afterwards, methods to improve the computing efficiency @cite_2 @cite_3 and accuracy @cite_16 @cite_17 @cite_21 were proposed. In 2007, Kim @cite_27 reformulated the iso-scallop tool path as geodesic parallel curves on the design surface by defining a new Riemannian metric.