## 1 Introduction  
Milling is one of the most used technologies to achieve the final shape of mechanical components due to its flexibility and accuracy. Process productivity has been increased during the last decades by exploiting the advancements in tooling system, machine structure and numerical control (NC). The latter, in synergy with modern CAD/CAM software, allows for the implementation of advanced toolpath strategies [1]. Traditionally, in 2.5-axis milling, two main strategies are used: direction-parallel and contour-parallel [2]. In pocket milling, other approaches can be pursued, such as zig-zag milling, or component-offset pattern [3]. All these strategies require algorithms to offset the final geometry to both compute the position of the center of the tool and, in case of multiple passes, to update the stock geometry. Several algorithms have been developed with the aim of improving efficiency and solve specific issues [4; 5; 6; 7; 8]. [PERSON] et al. [4] obtained the offset curve by trimming and jointing the raw curve, resulting from just projecting the points of the polyline. A similar approach was proposed by [PERSON] et al. [5] that exploits distance maps to trim local and global self-intersections, which are the main sources of errors in offset computation. [PERSON] [6] proposed to use a locus tracing concept for cutting radius offset and provides some applications to CNC machining. [PERSON] and [PERSON] [7] developed a method based on intersections of sculptured surfaces for offsetting point-sequence curves (PS- curves), while [PERSON] computed offset regions by using circles at each vertex and rectangles along each edge [8]. Contour offset can also be obtained by using a straight skeleton, but this could lead to sharp corners [9]. Linear axis is an interesting alternative as a means to compute such offsets, reducing the sharp corners issue, as investigated by [PERSON] and [PERSON] [9]. However, all the presented techniques are dedicated to uniform offset of a polyline curve, characterized by a constant distance of each offset element (i.e., segments) from the initial contour elements. Uniform offset is fundamental for most of the traditional toolpath approaches based on a geometric basis [10]. Nevertheless, in the case of advanced CAM strategies increasingly adopted, the limitation of constant value offset, i.e., uniform machining/stock allowance, could be critical. Indeed, in some cases variable radial engagement of the tool during the toolpath could be preferred, leading to the need of a non-uniform stock allowance on the component that could be achieved only with a non-uniform offset algorithm, i.e., offset where the distance to the initial contour varies along that input. Generally, such an approach is required when the toolpaths are not only calculated on a geometric basis (i.e., considering only the removal of the material), but also involving technological aspects. For example, in thin-wall milling, if stiffness of the part is considered in selecting the optimal engagement, non-uniform machining allowance on the components could be desired. This is the case of the approach proposed by [PERSON] et al. [11] that developed a cutting sequence algorithm to reduce workpiece deformation, suggesting the use of different depths of cut during the cutting cycle, depending on the changing stiffness of the part. Starting from such a concept, [PERSON] et al. [12] developed a method to compute the toolpath for milling thin-wall components. In their work, in each pass, the radial depth of cut changes continuously to achieve the desired quality without compromising productivity. To achieve this variable radial depth of cut, variable machining allowance on the component is required, and to implement such machining allowance on the final component a non-uniform offset algorithm is needed. Few works were dedicated to non-uniform offset, known also as variable-radius offset. [PERSON] et al.