以三維數位化儀分段量測物體之座標系統整合理論

The Coordinate System Integration Theorem Based on Section-by-section Measurement with 3D Digitizer

一般在沒有MicroScribe三維數位化儀的情況下，使用Rhino3D繪製模型時，必須以手工直接量測物體實際距離或是以拍照將圖片掃描入Rhino3D中進行描繪，這造成在繪製模型時不精準和緩慢的難處。但使用MicroScribe三維數位化儀手臂量測範圍會因實際物體太大而無法一次涵蓋，這導致另外一個量測困難。因此本文提出分段式量測法，來解決量測時所發生的障礙。配合所提出的座標系統整合理論、用Matlab計算出旋轉角度，再以Rhino旋轉結合後彩現。本研究發現用座標系統整合理論比Affine Map理論更能準確的處理座標的轉換問題。因為Affine Map會因MicroScribe的量測誤差而影響圖面整合的精準度，而本研究所提出的座標整合系統會自動調整量測的誤差，而使圖面的整合更逼近於實際物體。基於相同於量測大型物體之原理，本文使用小型之狗形頭顱作為量測物體來驗證座標系統整合方法。藉由本方法的提出，克服了上述繪製模型所可能引發的缺點，使繪製的模型精準、速度加快並且可以涵蓋大型物體。

Without using a 3D digitizer such as MicroScribe, manual measurement or scanning of photo image is used to input drawing data into the Rhino 3D and this results in problems of inaccuracy and slow-pace in the computer modeling. However, using the Microscribe has potential drawbacks too. It may not be able to take the measurements at one time and, thus, cause another problem. This paper proposes a section-by-section measurement to overcome the problem. Accompanying the coordinate system integration theorem and using Matlab as a tool to calculate the rotation angles around the x-y-z axes, one can rotate and render the model in Rhino. We found that our proposed theorem is far better than the affine map in dealing the transformation problems of coordinate systems. It is because affine map will be greatly influenced by the measurement errors of the Microscribe, which will jeopardize the accuracy of the integrated surfaces; but our proposed theorem will automatically adjust for measurement errors and fit the whole surfaces closer to the real artifact. Based on the same principle as applied to the large-scale measurement, we used a small dog-head artifact as a model to verify the coordinate system integration theorem. Through use of this theorem, we overcome the potential problems in computer modeling and speed up and improve the accuracy of the modeling. The method can also be applied to large-scale artifacts.