We propose a new volume reconstruction technique based on the six-direction cubic box-spline $M_6$. $M_6$ is $C^1$ continuous and possesses an approximation order of three, the same as that of the tri-quadratic B-spline but with much lower degree. In fact, $M_6$ has the lowest degree among the symmetric box-splines on ${\mathbb{Z}}^3$ with at least $C^1$ continuity. We analyze the polynomial structure induced by the shifts of $M_6$ and propose an efficient analytic evaluation algorithm for splines and their derivatives (gradient and Hessian) based on the high symmetry of $M_6$. To verify the evaluation algorithm, we implement a real-time GPU (graphics processing unit) isosurface raycaster which exhibits interactive performance (54.5 fps (frames per second) with $241^3$ dataset on $512^2$ framebuffer) on a modern graphics hardware. Moreover, we analyze $M_6$ as a reconstruction filter and state that it is comparable to the tri-cubic B-spline, which possesses a higher approximation order.

我们提出了一种新的基于六向三次箱样条的体积重建技术${米}_{\mathrm{6个}}$.${米}_{\mathrm{6个}}$是$C^{\mathrm{1个}}$连续且具有三阶近似，与三次 B 样条相同，但阶数低得多。实际上，${米}_{\mathrm{6个}}$在对称箱样条中具有最低的程度${\mathbb{Z}}^{\mathrm{3个}}$至少$C^{\mathrm{1个}}$连续性。我们分析了由移动引起的多项式结构${米}_{\mathrm{6个}}$并基于${米}_{\mathrm{6个}}$. 为了验证评估算法，我们实现了一个实时 GPU（图形处理单元）等值面光线投射器，它具有交互性能（54.5 fps（每秒帧数）$24{\mathrm{1个}}^{\mathrm{3个}}$上的数据集$51{\mathrm{2个}}^{\mathrm{2个}}$framebuffer）在现代图形硬件上。此外，我们分析${米}_{\mathrm{6个}}$作为重建滤波器，并声明它与三次 B 样条相当，后者具有更高的近似阶数。