Description

Seeing Parameters View plane: plane of our presentation surface Perspective reference point (VRP): main focus, all other survey parameters are communicated with respect to this point Perspective plane typical (VPN): look bearing Perspective separation: separation from camera to VRP

Transcripts

Seeing Parameters View plane: plane of our showcase surface View reference point (VRP): main focus, all other survey parameters are communicated in respect to this point View plane typical (VPN): look course View separation: separation from camera to VRP View-up heading: vector indicating top of camera View plane directions: film directions article directions: arranges that the items lie 240-422 Computer Graphics : Viewing in 3D_4

Viewing Parameters 240-422 Computer Graphics : Viewing in 3D_4

Conversion to View Plane Coordinates We wish to perform a progression of changes which will change the article organizes into the perspective plane directions. In the first place step: make an interpretation of the beginning to the right position for the perspective plane direction framework (moving to VRP then moving along the VPN by the VIEW-DISTANCE. Second step: adjust the z pivot 240-422 Computer Graphics : Viewing in 3D_4

3D Rotation around an Arbitrary Axis 1. Translate the hub to cause 2. Turn about x until the pivot of revolution is in the xz plane 3. Turn about y hub until the z hub relates to the hub of revolution 4. Pivot about z (hub of revolution) 5. Reverse the pivot about y 6. Reverse the pivot about x 7. Reverse the interpretation 240-422 Computer Graphics : Viewing in 3D_4

Graphical Illustrations 240-422 Computer Graphics : Viewing in 3D_4

Mathematical Illustrations Suppose the revolution hub is characterized by a point (x1, y1, z1) and a vector [A B C], so the line comparisons are x = Au + x1 y = Bu + y1 z = Cu + z1 The introductory interpretation lattice and its opposite interpretation are 240-422 Computer Graphics : Viewing in 3D_4

Mathematical Illustrations Rotation about x pivot V = (B 2 +C 2 ) 1/2 sin(I) = B/V cos(I) = C/V y (A, B, C) (0, B, C) (0, B, C) B V x I C z 240-422 Computer Graphics : Viewing in 3D_4

Mathematical Illustrations Rotation framework, Rx Reverse grid, Rx - 1 240-422 Computer Graphics : Viewing in 3D_4

Mathematical Illustrations Rotation about y L = (A 2 +B 2 +C 2 ) 1/2 V = (L 2 - A 2 ) 1/2 =(B 2 +C 2 ) 1/2 sin(J) = A/L cos(J) = V/L A x J L V z Rotation hub 240-422 Computer Graphics : Viewing in 3D_4

Mathematical Illustrations Rotation network, Ry Reverse network, Ry - 1 240-422 Computer Graphics : Viewing in 3D_4

Mathematical Illustrations Rotation about the z hub The real change for a turn around an arbitraty hub is given by R = T - 1 R x - 1 R y - 1 R z R y R x T 240-422 Computer Graphics : Viewing in 3D_4

Back to âView Plane Coordinates Conversionâ Parameters: VPR = (x r , y r , z r ) VPN = [N x , N y , N z ] View-up = [x up , y up , z up ] View-separation = VD The whole change is TMATRIX = R z R y R x T 240-422 Computer Graphics : Viewing in 3D_4

Mathematical Illustrations V=(N y 2 + N z 2 ) 1/2 240-422 Computer Graphics : Viewing in 3D_4

Mathematical Illustrations 240-422 Computer Graphics : Viewing in 3D_4

Clipping in 3D Clipping against planes, not against lines as in 2D Front plane cut-out Back plane cut-out Top plane cut-out Bottom plane cutting Left plane cutting Right plane cut-out Clipping Process 240-422 Computer Graphics : Viewing in 3D_4

3D Clipping Fig 8-38, 8-39, 8-40 240-422 Computer Graphics : Viewing in 3D_4

3D Clipping 240-422 Computer Graphics : Viewing in 3D_4

Front and Back Clipping for the point (x1, y1, z1) to be noticeable: z1<= FRONT-Z and z1 >= BACK-Z 240-422 Computer Graphics : Viewing in 3D_4

3D Viewing Transformation Summary 1. Draw article in the item arranges 2. Specify review parameter (VPR, VPN, VD, and so on.) 3. Convert article directions to view plane directions 4. Perform 3D cutting 5. Project the items in survey onto the perspective plane 240-422 Computer Graphics : Viewing in 3D_4

3D Application: Flight Simulator Fig 8-45, 8-46 240-422 Computer Graphics : Viewing in 3D_4

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