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1、1ViewShandong University Software College2ObjectivesIntroduce the classical viewsCompare and contrast image formation by computer with how images have been formed by architects,artists,and engineersLearn the benefits and drawbacks of each type of viewIntroduce the mathematics of projectionIntroduce
2、OpenGL viewing functionsLook at alternate viewing APIsView3We call the pictures for observing objects with different ways are views.View results are related with the shape and size of scene objects,the position and direction of viewpoint.4Classical Viewing Viewing requires three basic elements One o
3、r more objects A viewer with a projection surface Projectors that go from the object(s)to the projection surface Classical views are based on the relationship among these elements The viewer picks up the object and orients it how she would like to see it Each object is assumed to constructed from fl
4、at principal faces Buildings,polyhedra,manufactured objects5Planar Geometric Projections Standard projections project onto a plane Projectors are lines that either converge at a center of projection are parallel Such projections preserve lines but not necessarily angles Nonplanar projections are nee
5、ded for applications such as map construction63D space2D imageProjectionZXpYpWindow Window coordinatecoordinateScreen coordinate systemScreen coordinate systemWorld coordinate systemWorld coordinate systemViewportViewportWindowWindowFar planeNear planeViewpointI m a g e planeViewing VolumeViewing Vo
6、lume7Classical Projections8Perspective vs ParallelComputer graphics treats all projections the same and implements them with a single pipelineClassical viewing developed different techniques for drawing each type of projectionFundamental distinction is between parallel and perspective viewing even t
7、hough mathematically parallel viewing is the limit of perspective viewing9Taxonomy of Planar Geometric ProjectionsparallelperspectiveAxonometric multivieworthographicobliqueIsometricDimetric trimetric2 point1 point3 pointplanar geometric projections10Perspective Projection11Parallel Projection12Orth
8、ographic ProjectionProjectors are orthogonal to projection surfaceArguably the simplest projectiono Image plane is perpendicular to one of the coordinate axes;o Project onto plane by dropping that coordinate;o All rays are parallel.13Multiview Orthographic Projection Projection plane parallel to pri
9、ncipal face Usually form front,top,side viewsisometric(not multivieworthographic view)frontsidetopin CAD and architecture,we often display three multiviews plus isometric 14Advantages and DisadvantagesPreserves both distances and angles Shapes preserved Can be used for measurements Building plans Ma
10、nualsCannot see what object really looks like because many surfaces hidden from view Often we add the isometric15Axonometric ProjectionsAllow projection plane to move relative to objectclassify by how many angles ofa corner of a projected cube are the samenone:trimetrictwo:dimetricthree:isometricq 1
11、q 3q 216Types of Axonometric Projections17Advantages and Disadvantages Lines are scaled(foreshortened)but can find scaling factors Lines preserved but angles are not Projection of a circle in a plane not parallel to the projection plane is an ellipse Can see three principal faces of a boxlike object
12、 Some optical illusions possible Parallel lines appear to diverge Does not look real because far objects are scaled the same as near objects Used in CAD applications18Oblique Projection Arbitrary relationship between projectors and projection plane19Advantages and Disadvantages Can pick the angles t
13、o emphasize a particular face Architecture:plan oblique,elevation oblique Angles in faces parallel to projection plane are preserved while we can still see“around”side In physical world,cannot create with simple camera;possible with bellows camera(波纹管相机)or special lens(architectural)20Perspective Pr
14、ojectionProjectors converge at center of projectionNaturally we see things in perspectiveo Objects appear smaller the farther away they are;o Rays from view point are not parallel.21Vanishing Points Parallel lines(not parallel to the projection plan)on the object converge at a single point in the pr
15、ojection(the vanishing point)Drawing simple perspectives by hand uses these vanishing point(s)vanishing point22Three-Point Perspective No principal face parallel to projection plane Three vanishing points for cube23Two-Point Perspective On principal direction parallel to projection plane Two vanishi
16、ng points for cube24One-Point Perspective One principal face parallel to projection plane One vanishing point for cube25Advantages and Disadvantages Objects further from viewer are projected smaller than the same sized objects closer to the viewer(diminution)Looks realistic Equal distances along a line are not projected into equal distances(nonuniform foreshortening)Angles preserved only in planes parallel to the projection plane More difficult to construct by hand than parallel projections(but
