Apparent contours of nonsingular real cubic surfaces

Reconstruction of rational ruled surfaces from their silhouettes

We provide algorithms to reconstruct rational ruled surfaces in three-dimensional projective space from the `apparent contour' of a single projection to the projective plane. We deal with the case of tangent developables and of general projections to $\mathbb{p}^3$ of rational normal scrolls. In the first case, we use the fact that every such surface is the projection of the tangent developable of a rational normal curve, while in the second we start by reconstructing the rational normal scroll. In both instances we then reconstruct the correct projection to $\mathbb{p}^3$ of these surfaces by…

利用代数几何从标定相机图像重建Darboux四次圆纹曲面

Using Algebraic Geometry to Reconstruct a Darboux Cyclide from a Calibrated Camera Picture

本文利用Darboux四次圆纹曲面沿绝对二次曲线的奇点性质，从标定相机图像的表观轮廓恢复其齐次方程，实现欧氏相似变换下的曲面识别。