【正文】
ble objects from anomalous but realizable pictures interactively by the following steps. First, we find a picture with hidden lines that is anomalous but still realizable. For this purpose, we employ the junction dictionary for pictures with hidden lines ~13) and Theorems 1 and 2 described in previous sections. Once an anomalous but realizable picture is found, the system of equations (1) and inequalities (2) tells us the minimum set of vertices such that if we give the depth ofthese vertices, the whole structure of the polyhedron is specified uniquely. Then, we choose the viewpoint re lative to the picture。 line data extracted from real images are far from perfect line drawings treated in this theory. Actually there is a great gap between real noisy data and perfect line drawings, and it seems difficult to utilize the pictureinterpretation theory directly for real image processing. However, this does not mean that the pictureinter pretation theory is practically useless. As an example, we present in this paper a new application of the picture interpretation theory to the design of children39。 邊界 在這個(gè)圖 片中 顯示 為 點(diǎn) , 這兩點(diǎn)的對(duì)象應(yīng)該是 2個(gè) 圓大小相同,而且 應(yīng)該互相接觸。為此,我們采用 交界字 典圖片與隱藏線 ~13)和 前面描述的理論 1和理論 2。從 物質(zhì) 的角度來(lái)看,在另一方面,多面體是 不規(guī)則的表面是可以實(shí)現(xiàn)的 。 哈夫曼編碼( 5)和克勞夫斯( 1)建造的完整列表可能的組合的標(biāo)簽在這路口;名單現(xiàn)在稱為聯(lián)接詞典。 在 Z=1這個(gè)面畫一條直線 D,我們 認(rèn)為如果 D是一個(gè)多面體在這個(gè)三維空間里的投影,那么直線 D在這個(gè) 坐標(biāo)系統(tǒng) 的 三維空間 里存在的。我們 在本文中 提出了 釋圖理論的 一個(gè)新的應(yīng)用 — 兒童玩具設(shè)計(jì)。本文提出了一個(gè)交互式系統(tǒng)生成展開表面的對(duì)象,系統(tǒng)輸出被用來(lái) 實(shí)現(xiàn) 作為 不可能實(shí)現(xiàn)物體的兒童 玩具 。本原因之二是,問(wèn)題本身是太理想化了 很難 被應(yīng)用到實(shí)際 。本系統(tǒng)的輸出 可以應(yīng)用在為 孩子構(gòu)建 “ 不可能 ” 的對(duì)象 的材料 。一個(gè)邊緣被稱為凸如果相關(guān)的兩側(cè)面形成山脊沿著這條邊,如果他們形成一個(gè)凹谷。讓我們 想象 一個(gè)多面體 便面,我們會(huì)發(fā)覺(jué) 如果它是由 幾個(gè) 相互垂直的 矩形表面拼接而成 。因此,這些產(chǎn)生的一種新型的光幻覺(jué)。 最后一步是繪制圖的展開表面。 in revised form 12 August 1996。 we assign the label to this line. A line is called a convex line if it is the image of a convex edge and if the associated side faces are both visible。) and (b) show the unfolded surfaces of the three pieces of the object represented by the picture in Fig. 5(b). Figure 7(a) and (a39。) are the photographs of the same objects taken from another viewpoint. 5. CONCLUDING REMARKS We have described an interactive system for generating polyhedra from anomalous pictures and for drawing the unfolded surfaces of them. The output of the system can be used as toys with which children make impossible objects. These toys may give children a chance to learn empirically about spatial geometry and visual perception. AcknowledgementsThis work is supported by Hayao Na kayama Foundation for Science, Technology and Culture. 。 thus we get the plete description of the poly hedron. The final step is to draw the figure of the unfolded surface