Degree elevation is a typical corner-cutting algorithm. It refers to the process transforming control polygons when embedding a polynomial space of some degree into any polynomial space of higher degree. Dimension elevation similarly refers to the transformation of control polygons when embedding an Extended Chebyshev space possessing a Bernstein basis into another one, of higher dimension. Unlike degree elevation, this cannot always be split into successive (corner-cutting) steps elevating the dimension by one. What happens when it is not possible is investigated here. We shall see that the new control points can even be located outside the initial control polygons, giving evidence that dimension elevation is not always corner-cutting.

度高是一种典型的切角算法。它是指将某种程度的多项式空间嵌入到任何更高程度的多项式空间中时变换控制多边形的过程。尺寸高程类似地是指将具有伯恩斯坦基础的扩展切比雪夫空间嵌入到另一个具有更高尺寸的空间时，控制多边形的变换。与度高不同，不能总是将其分成连续的（角切割）步骤，以将尺寸提升一倍。在这里研究不可能的情况。我们将看到，新的控制点甚至可以位于初始控制多边形的外部，这表明尺寸标注并不总是切角。