CATIA study,曲面优化工具命令,Working With the Generative Shape Optimizer Workbench,Bump,Wrap Curve,Wrap Surface,Shape Morphing,曲面优化工具命令,Bump,Before,After,变形中心：中心点处变形量最大，向外渐变，直至边界处为,0,变形方向：缺省为曲面法向变形距离：中心点沿变形方向的最大变形距离曲面鼓包（,Bump,）：通过变形生成鼓包需定义变形范围，变形中心点，变形方向，变形大小变形边界：必须是落在曲面上的曲线变形边界连续性：变形鼓包在边界处与原始曲面的连续性，可以是点连续，切矢连续，曲率连续投影方向：若变形中心点不在曲面上，则将该点沿投影方向向曲面投影得到的点作为实际变形中心中心曲率：缺省为,1,（图示,A,）；,1,，面型趋于陡峭（图示,C,）This task shows how to deform surfaces basing the deformation on curve wrapping,that is matching each reference curve onto a target curve.The deformation is then defined by the transformation of the reference curves into target curves.,根据曲线变形（,Wrap curve,）：参考两个已知曲线的相对关系对原始曲面进行变形，从而得到变形结果。
已知曲线不必落在原始曲面上曲面优化工具命令,Wrap Curve,先选参考曲线，再选目标曲线，不能打乱，选完一对后在此显示You must always select successively a reference then a target curve to define a pair.You cannot select all reference curves,then all target curves for example.,When several pairs of curves are selected,they must be ordered,not randomly selected.,多组线的选择须注意顺序,Reference curves should not intersect each other,nor should the target curves should intersect each other.,参考曲线之间或目标曲线之间不能相交Reference and target curves can be multi-cells.Joined,blended,or matched curves,for example,can be used as reference or target curves.,参考曲线或目标曲线可以是组合曲线。
Before,After,Curve Wrapping Deformation with Fixed Reference,曲线变形之固定参考曲线：,考虑到在很多场合下，需要与周边曲面保持连续性，此时可以使用通过固定参考曲线，并指定连续类型，点连续，切矢连续或曲率连续具体操作,：选择参考曲线后，将鼠标移至“,ReferenceXXX,”,字样上，右键弹出下拉菜单，并选择“,Fixed reference curve”,，同时在对话框里将自动跳过目标曲线的配对，直接换行进入下一个配对的选择，如下图并不只是首末参考曲线能设置固定，中间的也可以，只是不能进行连续性约束曲面优化工具命令,Wrap Curve,目标曲线空出,连续性的选择,右键弹出菜单,也可以在此勾选，效果一样,Editing a Deformed Surface,曲线变形之修改编辑：,包括增加或移除参考曲线,-,目标曲线配对，固定参考曲线，添加约束等关于约束,：只可以对首末参考曲线进行连续性的约束，但不能保证完全约束到位，有时可能只是近似曲面优化工具命令,Wrap Curve,Ref1,：固定，曲率,Ref3,：固定,Ref2,：,无目标曲线,无目标曲线,曲面优化工具命令,Wrap Curve,关于脊线,：默认第一条参考曲线即为脊线，但脊线若过短，如小于曲面的边界框，则系统会自动延长脊线，相应的其它配对曲线也会自动作延长。
也可以选择已知曲线作为脊线关于投影方向,：在下一页有具体描述系统自动计算方法：脊线与法平面的交点为,P1,，最后一条参考曲线与法平面的交点为,P2,，投影方向定义为在法平面内，,P1,P2,连线的垂直方向How Is the Deformation Computed?,The deformation is computed in each plane,P,normal to the spine.By default the spine is the first reference curve,but you can select a new spine using the,Spine,field in the,Reference,tab.,In each plane,P,the system computes the intersection between the plane and each curve.A curve(,Cr,)is created between the first intersection point(,Ir 1,)and the last intersection point(,Ir n,)on reference curves,passing through all the intersection points between these two.Similarly,a curve(,Ct,)is created passing through all the intersections points between the first(,It 1,)and the last intersection point(,It n,)on target curves.,Then,for each point,Q,resulting from the intersection of the surface to be deformed with the plane,Q,is projected onto the curve,Cr,according to the projection direction(,dir,).This projection direction is the vectorial product of:vector(,lspine,lr2,)vector normal to,P,.The result of the projection of point,Q,is the point,Qr,which parameter on,Cr,is,v,.Similarly,a point,Qt,is created on the curve,Ct,with the same v parameter as point,Qr,on curve,Cr,.,Then,Qd,that is the transformation of point,Q,according to the wrap curve deformation,is obtained by adding:,Q+vector(Qr,Qt),曲面优化工具命令,Wrap Curve,3D view,where:,r1,r2 are the reference curves,t1,t2 are the target curves,P is a plane normal to the spine,Planar view,where:,Ir1:is the intersection between P and r1,Ir2:is the intersection between P and r2,It1:is the intersection between P and t1,It2:is the intersection between P and t2,曲面优化工具命令,Wrap Curve,3D view,where:,r1,r2 are the reference curves,t1,t2 are the target curves,P is a plane normal to the spine,Planar view,where:,Ir1:is the intersection between P and r1,Ir2:is the intersection between P and r2,It1:is the intersection between P and t1,It2:is the intersection between P and t2,曲线变形之原理：,首先，所有的变形都在脊线的法平面内进行。
所有参考曲线与法平面的交点连线记为,Cr,，所有目标曲线与法平面的交点连线记为,Ct,；,脊线与法平面的交点记为,Is,，最后一条参考曲线与法平面的交点记为,In,，方向,dir,与“,Is,In”,连线垂直；,曲面与法平面的交线的任意一点记为,Q,，将,Q,沿方向,dir,向,Cr,投影，得到,Qr,，,Qr,在,Cr,上的位置记为,v,；,根据,V,值，在,Ct,上找到,Qt,点，将,Qr,Qt,记为矢量,V,；,以,Q,为起点，根据矢量,V,，得到最终变形点,Qd,Q,的投影点,Qr,，其在曲线上的位置记为,v.,Cr,Ct,Before,After,Wrap Surface,：,Deforming Surfaces According to Surface Wrapping,This task shows how to deform surfaces basing the deformation on the projection of the element to be deformed onto two definition surfaces.,根据曲面变形（,Wrap surface,）：根据两个已知曲面的关系产生变形，从而得到变形结果。
曲面优化工具命令,Wrap Surface,Before,After,共有,3,种曲面变形方式：,3D,：,Normal,：,With direction,：,3D,Normal,With direction,3D,变形法：以一点,A,为例，,将点,A,往参考曲面上投影得到投影点,B,自动寻找点,B,在目标曲面上的匹配点,C,，直线段,BC,即为变形距离值,记为,L,将点,A,沿,BC,方向平移,L,，即得到变形点,D,曲面优化工具命令,Wrap Surface,曲面变形方式之,3D,：,曲面变形方式之,Normal,：,Normal,变形法：以一点,A,为例，,将点,A,往参考曲面上投影得到投影点,B,，直线段,BC,即为变形距离值,记为,L,自动寻找点,B,在目标曲面上的匹配点,C,将点,C,沿该点法向平移,L,，即得到变形点,D,The deformed point is computed as follows:Q=P+(Pts-Prs),You need to select a deformation direction(here Plane.1):,曲面优化工具命令,Wrap Surface,曲面变形方式之,With direction,：,3D,变形法：以点,P,为例，,。