OverCoatanimplicitcanvasfor3Dpainting隐式曲面三维画布.docxVIP

OverCoat: an implicit canvas for 3D painting隐式曲面三维画布 主讲：钱博磊 2011-10-19 2D到3D的转化 stroke embedding 笔画的定义 stroke 3D画布的定义 3D canvas scalar field： f： R3 - R A point x with f(x) = l is said to lie on level l. proxy geometry 2D到3D的转化 stroke embedding 距离约束 角度约束 长度约束 绘制模式 objective terms level set tool: wlevel = 1 wangle =0.1 wlength = 0 hair feather tool: wlevel = 1/0 wangle= 1 wlength = 0.05 求解 quasi-Newton L-BFGS 非线性问题的最优解 数据初始化 initialization the system initializes the unknows to lie on the frontmost target level set of the scalar field using sphere tracing ,a ray marching technique 2. only the first and the last stroke points are initialized to their target levels 数据优化 refinement 出现不理想的初始化数据 -- 通过插入中值点进行优化 迭代过程 求解的过程需要反复计算以下数值  field’s magnitude f(x) - 点x距proxy geometry的最小距离  the gradient f - 所求点x与画布上离他最近点间的单位向量  the derivative of the scalar field - f(pi)/ti = f  di 绘制 rendering 将映射到3D的笔画投影回2D显示屏的过程 需要确保实时和笔画间位置关系的稳定 全局上， 按深度排序 局部上， 按绘制先后顺序排序 附带工具 – 3D画布的修改 sculpturing kj： sculpture stroke 的力度和方向 the lower part of the fraction is the Lipschitz constant of the signed distance field of the proxy geometry (which is equal to 1) plus the Lipschitz constant of the sum of all contributions of the sculpting strokes