3D Geometric Transformation课件.ppt

3D Geometric Transformation Point in 3D space Position (x, y, z) Color (r, g, b) Normal (Nx, Ny, Nz) Homogenous Coordinates Position (x,y,z,w) Usually (x,y,z,1) Transformations Translation Scaling Rotation Projection (x,y,z) N 漳填歧吏循宗洪或衰矛紫慨掇专予懒牵查厅朝甸睹膀淫注呕吮既自术慰哀3D Geometric Transformation课件3D Geometric Transformation课件 3D Translation (x,y,z) (x’,y’,z’) T(dx,dy,dz)= 1 0 0 dx 0 1 0 dy 0 0 1 dz 0 0 0 1 To translate the point (x,y,z) by the offset (dx, dy, dx) T(dx,dy,dz) . (x,y,z,1)T =(x+dx, y+dy, z+dz,1) 洼卜萄点掷状劲导悉瘩脯是梯萎疾快惟陕宪固语悸藩饼聊存府奄综脓威离3D Geometric Transformation课件3D Geometric Transformation课件 3D Scaling (x,y,z) (x’,y’,z’) S(sx,sy,sz)= sx 0 0 0 0 sy 0 0 0 0 sz 0 0 0 0 1 To scale the vector (x,y,z) by the factors sx,sy,and sz S(sx,sy,sz) . (x,y,z,1)T =(x*sx, y*sy, z*sz,1) 詹粱筷茂修酌屑冠请跳厕擒工经窗挑烈例书寝欲罩短镶流满煌碳琼甭缆曹3D Geometric Transformation课件3D Geometric Transformation课件 3D Sheering (x,y,z) (x’,y’,z’) Sz(hx,hy)= 1 0 hx 0 0 1 hy 0 0 0 1 0 0 0 0 1 To sheer the point (x,y,z) along the x and y axes H(hx,hy) . (x,y,z,1)T = (x+hx*z, y+hy*z, z, 1) Sheer along one or more axes 净蔽挟崩揽乏咬阴技潘邱擎二别彤涧隆挽惫促平泳昔伯丝森贼醒司硷闯群3D Geometric Transformation课件3D Geometric Transformation课件 3D Rotation (x,y,z) (x’,y’,z’) Rx(j) = 1 0 0 0 0 cos(j) -sin(j) 0 0 sin(j) cos(j) 0 0 0 0 1 A 90o Rotation of (0,1,0,1) will produce (0,0,1,1) To rotate a point (x,y,z) around the x axis by angle j x 诈栈痈诸乏豹蹋码惯瘫髓塞鞋匡头寡约骚难胁州蔚累浦痉寸黍毡命描噎锄3D Geometric Transformation课件3D Geometric Transformation课件 3D Rotation (x,y,z) (x’,y’,z’) Ry(j) = cos(j) 0 sin(j) 0 0 1 0 0 -sin(j) 0 cos(j) 0 0 0 0 1 A 90o Rotation of (1,0,0,1) will produce (0,0,1,1) To rotate a point (x,y,z) around the y axis by angle j 延啡颗哄岩弗芭挪祈孟迪谣咎怯宝碱澎眶廉符峙蝇甚订良弗少欣十铲墟穗3D Geometric Transformation课件3D Geometric Transformation课件 3D Rotation (x,y,z) (x’,y’,z’) Rz(j) = cos(j) -sin(j) 0 0 sin(j) cos(j) 0 0