Viewing. Perspective views. Parallel l views. Finite COP (center of projection) COP at infinity DOP (direction of projection) Parallel View

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1 Viewing 3 r Week, 29 Funamental Tes of Viewing views Finite COP (center of rojection) Parallel l views COP at infinit DOP (irection of rojection) View Parallel View

2 Parallel View View

3 Taonom of Planar Geometric Projections Planar Geometric Projections Parallel Orthograhic Aonometric Oblique oint 2 oint 3 oint Isometric Dimetric Trimetric Projection

4 Parallel Projection Orthograhic Projections Projectors are erenicular to the rojection lane Isometric Front Orthograhic Projections To Sie Temle an Three Multi-view i Orthograhic Projections

5 Avantages an Disavantages Preserving both istances an angles Shaes reserve Can be use for measurements Builing lans Manuals Cannot see what object reall looks like because man surfaces hien from view Often we a the isometric i Aonometric Projections () Projection lane can have an orientation with resect to the object Projectors are still orthogonal to the rojection lanes Construction To View Sie View

6 Aonometric Projections (2) Preserving arallel lines but not angles Isometric rojection lane is lace smmetricall with resect to the three rincial faces Dimetric two of rincial faces Trimetric general case Aonometric Projections (2) Preserving arallel lines but not angles Isometric rojection lane is lace smmetricall with resect to the three rincial faces Dimetric two of rincial faces Trimetric general case

7 Oblique Projections Projectors can make an arbitrar angle with the rojection lane Preserving angels in lanes arallel to the rojection lane Construction To View Sie View Projections () Projectors converge at the center of rojection

8 Projections (2) One-, two-, an three-oint ersectives Vanishing oints arallel lines (not arallel to the rojection lane) on the object converge at a single oint in the rojection Three-Point Two-Point One-Point Projections (2) One-, two-, an three-oint ersectives Vanishing oints arallel lines (not arallel to the rojection lane) on the object converge at a single oint in the rojection Three-Point Two-Point One-Point

9 Projections (2) One-, two-, an three-oint ersectives Vanishing oints arallel lines (not arallel to the rojection lane) on the object converge at a single oint in the rojection Three-Point Two-Point One-Point Projections (2) One-, two-, an three-oint ersectives Vanishing oints arallel lines (not arallel to the rojection lane) on the object converge at a single oint in the rojection Three-Point Two-Point One-Point

10 Avantages an Disavantages Objects further from viewer are rojecte smaller than the same sie objects closer to the viewer (iminution) Looking realistic Equal istances along a line are not rojecte into equal istances (nonuniform foreshortening) Angle reserve onl in lane arallel to the rojection lane More ifficult to construct b han than arallel rojections (but not more ifficult b comuter) Comuting Viewing Three asects of the viewing rocess, all of which are imlemente in the ieline Positioning the camera Setting the moel-view matri Selecting a lens Setting the rojection matri Cliing Setting the view volume

11 The OenGL Camera In OenGL, initiall the object an camera frame are same Default moel-view matri is an ientit The camera is locate at origin i an oints in the negative -irection OenGL also secifies a efault view volume A cube with sies of length 2 centere at the origin Default rojection matri is an ientit Default Projection Default rojection is orthogonal clie out

target-osition, t an u-vector Look-At Positioning Angle of view Projections in OenGL Onl objects that

12 Look-At Function The GLU librar contains the function To form the require moel-view matri glmatrimoe( GL_MODELVIEW ); glloaientit( ); glulookat(ee, ee, ee, at, at, at, u, u, u); Ee-osition, target-osition, t an u-vector Look-At Positioning Angle of view Projections in OenGL Onl objects that fit within the angle of view of the camera aear in the image View volume Being clie out of scene Frustum: truncate rami

Parallel in OenGL Orthograhic viewing function glmatrimoe(gl_projection); glloaientit( ); glortho(min, ma, min, ma, near, far); OenGL rovies onl this arallel-viewing l i function near < far!

13 Parallel in OenGL Orthograhic viewing function glmatrimoe(gl_projection); glloaientit( ); glortho(min, ma, min, ma, near, far); OenGL rovies onl this arallel-viewing l i function near < far!! no restriction ti on the sign ma far min near in OenGL () Secification of a frustum glmatrimoe(gl_projection); glloaientit( ); glfrustum(min, ma, min, ma, near, far); near, far: ositive number!! ma far min near

in OenGL (2) Secification using the fiel of view glmatrimoe(gl_projection); glloaientit( ); glu(fov, asect, near, far); fov: : the angle between to an bottom lanes (in the u ()irection) asect: with

14 in OenGL (2) Secification using the fiel of view glmatrimoe(gl_projection); glloaientit( ); glu(fov, asect, near, far); fov: : the angle between to an bottom lanes (in the u ()irection) asect: with ivie b height h Projections an Normaliation The efault rojection in the ee (camera) frame Oth Orthogonal For oints within the efault view volume: View normaliation,, All other views are converte to the efault view b transformations that etermine the rojection matri To allow use of the same ieline for all views Most grahics sstems use

Simle Orthogonal Projections Simle Orthogonal Projections Projectors are erenicular to the view lane Projectors are erenicular to the view lane Orthograhic rojection matri w Simle Projections ()

15 Simle Orthogonal Projections Simle Orthogonal Projections Projectors are erenicular to the view lane Projectors are erenicular to the view lane Orthograhic rojection matri w Simle Projections () Simle Projections () Simle camera Simle camera Projection lane is orthogonal to ais Projection lane in front of COP Projection lane in front of COP,,, /, / Three-Dimensional View To View Sie View

16 Simle Projections (2) Simle Projections (2) Homogeneous coorinates Homogeneous coorinates w / / w w / / rojection matri w / / rojection matri / M Projection Pieline Moel-View Moel-View Projection Projection Division Division / Division Division If w we must ivie b w to return from If w, we must ivie b w to return from homogeneous coorinates Th ti i i i ti i i i i l th i The ersective ivision ersective ivision iels the esire ersective equations w w

Viewing. Perspective views. Parallel l views. Finite COP (center of projection) COP at infinity DOP (direction of projection) Parallel View

Viewing. Perspective views. Parallel l views. Finite COP (center of projection) COP at infinity DOP (direction of projection) Parallel View Viewing th Week, 29 Funamental Tes of Viewing views Finite COP (center of rojection) Parallel l views COP at infinit DOP (irection of rojection) View Parallel View Parallel View View Classical Viewing