Viewing
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计算机图形学讲义－10
Viewing (I)
姜明 北京大学数学科学学院
Based on [EA], Chapter 5.
更新时间2011年12月30日星期五1时16分13秒
计算机图形学讲义－10
Outline
• Classical and Computer Viewing • Viewing with a Computer • Positioning of the Camera • Simple Projections • Projections in OpenGL
vanishing point
Angel: Interactive Computer Graphics 5E © Addison-Wesley 2009
11
计算机图形学讲义－10
Three-Point Perspective
• No principal face parallel to projection plane • Three vanishing points for cube
Angel: Interactive Computer Graphics 5E © Addison-Wesley 2009
13
计算机图形学讲义－10
One-Point Perspective
• One principal face parallel to projection plane • One vanishing point for cube
计算机图形学讲义－10
Synthetic-camera Model
• • • • The projectors meet at the centre of projection (COP). The COP corresponds to the center of the lens in the camera or in the eye. It is the origin of the camera frame in graphics systems. The projection surface is a plane. The projectors are straight lines, based on geometric optics. The class of projections is also called planar geometric projections. As the COP is moved to infinity, the projectors become parallel and the COP can be replaced by a direction of projection (DOP). Views with a finite COP are called perspective views. Views with a COP at infinity is called parallel views.
Orthographic projections
Temple and three multiview orthographic projections
计算机图形学讲义－10
Axonometric Projection
• 轴测投影
(a) Construction of trimetric-view projection; (b) top view; (c) side view.
计算机图形学讲义－10 • Its desired location is centered at a point called the view-reference point (VRP), given in the world frame. Its orientation is specified by the view-plane normal (VPN) and view-up vector (VUP).
– This is the job of the model-view transformations, – After vertices pass through this transformation, they are in the camera frame.
• 2nd step is the application of the projection transformation.
– VPN gives the orientation of the projection plane, or back of the camera. – VUP fixes the projection plane or the back of the camera.
•
•UP vector on the view plane to obtain the up-direction vector v. We can compute a 3rd orthogonal direction u. This new orthogonal system is called the viewing-coordinate system or the u-v-n system. It is the camera frame with the addition of the VRP. The final transformation matrix.
计算机图形学讲义－10
Positioning of the Camera
• Our starting point is the world frame. • We describe the camera’s position and orientation in this frame. • The precise type of image that we wish to obtain – perspective or parallel – is determined separately by the projection matrix in OpenGL, the normalization transformation. • The camera is positioned initially at its default location and orientation, pointing to the negative zdirection.
Angel: Interactive Computer Graphics 5E © Addison-Wesley 2009
14
计算机图形学讲义－10
Advantages 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 not more difficult by computer)
•
• •
计算机图形学讲义－10
• Computer graphics systems have two fundamental types of viewing (parallel and perspective). • Classical graphics appears to permit a host of different views. • Classical viewing intends to show a specific relationship among an object, the viewer and the projection plane. • Computer graphics systems prefers complete independence of all specifications.
Angel: Interactive Computer Graphics 5E © Addison-Wesley 2009
10
计算机图形学讲义－10
Vanishing Points
• Parallel lines (not parallel to the projection plan) on the object converge at a single point in the projection (the vanishing point) • Drawing simple perspectives by hand uses these vanishing point(s)
计算机图形学讲义－10
Classical Viewing
Each classical view is determined by the specific relationship between the objects and viewer.
计算机图形学讲义－10
Orthographic Projections
Angel: Interactive Computer Graphics 5E © Addison-Wesley 2009
12
计算机图形学讲义－10
Two-Point Perspective
• On principal direction parallel to projection plane • Two vanishing points for cube
计算机图形学讲义－10
Classical and Computer Viewing
• • • • • Classical Viewing Orthographic Projections Axonometric Projections Oblique Projections Perspective Viewing
计算机图形学讲义－10
Oblique Projections
(a) Construction of oblique view projection; (b) top view; (c) side view.
计算机图形学讲义－10
Perspective Projection
• Projectors coverge at center of projection
– It applies the specified projection – orthographic or perspective – to the vertices and puts objects within the specified clipping volume in a normalized clipping volume. • Default camera in OpenGL – the camera is at the origin, – pointing to the negative zdirection, – orthographic view, – Clipping volume centered at the origin, of side length 2.
Angel: Interactive Computer Graphics 5E © Addison-Wesley 2009
15
计算机图形学讲义－10
Viewing with a Computer
• Viewing consists of two fundamental operations. • 1st we must position the camera.
Viewing (I)
姜明 北京大学数学科学学院
Based on [EA], Chapter 5.
更新时间2011年12月30日星期五1时16分13秒
计算机图形学讲义－10
Outline
• Classical and Computer Viewing • Viewing with a Computer • Positioning of the Camera • Simple Projections • Projections in OpenGL
vanishing point
Angel: Interactive Computer Graphics 5E © Addison-Wesley 2009
11
计算机图形学讲义－10
Three-Point Perspective
• No principal face parallel to projection plane • Three vanishing points for cube
Angel: Interactive Computer Graphics 5E © Addison-Wesley 2009
13
计算机图形学讲义－10
One-Point Perspective
• One principal face parallel to projection plane • One vanishing point for cube
计算机图形学讲义－10
Synthetic-camera Model
• • • • The projectors meet at the centre of projection (COP). The COP corresponds to the center of the lens in the camera or in the eye. It is the origin of the camera frame in graphics systems. The projection surface is a plane. The projectors are straight lines, based on geometric optics. The class of projections is also called planar geometric projections. As the COP is moved to infinity, the projectors become parallel and the COP can be replaced by a direction of projection (DOP). Views with a finite COP are called perspective views. Views with a COP at infinity is called parallel views.
Orthographic projections
Temple and three multiview orthographic projections
计算机图形学讲义－10
Axonometric Projection
• 轴测投影
(a) Construction of trimetric-view projection; (b) top view; (c) side view.
计算机图形学讲义－10 • Its desired location is centered at a point called the view-reference point (VRP), given in the world frame. Its orientation is specified by the view-plane normal (VPN) and view-up vector (VUP).
– This is the job of the model-view transformations, – After vertices pass through this transformation, they are in the camera frame.
• 2nd step is the application of the projection transformation.
– VPN gives the orientation of the projection plane, or back of the camera. – VUP fixes the projection plane or the back of the camera.
•
•UP vector on the view plane to obtain the up-direction vector v. We can compute a 3rd orthogonal direction u. This new orthogonal system is called the viewing-coordinate system or the u-v-n system. It is the camera frame with the addition of the VRP. The final transformation matrix.
计算机图形学讲义－10
Positioning of the Camera
• Our starting point is the world frame. • We describe the camera’s position and orientation in this frame. • The precise type of image that we wish to obtain – perspective or parallel – is determined separately by the projection matrix in OpenGL, the normalization transformation. • The camera is positioned initially at its default location and orientation, pointing to the negative zdirection.
Angel: Interactive Computer Graphics 5E © Addison-Wesley 2009
14
计算机图形学讲义－10
Advantages 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 not more difficult by computer)
•
• •
计算机图形学讲义－10
• Computer graphics systems have two fundamental types of viewing (parallel and perspective). • Classical graphics appears to permit a host of different views. • Classical viewing intends to show a specific relationship among an object, the viewer and the projection plane. • Computer graphics systems prefers complete independence of all specifications.
Angel: Interactive Computer Graphics 5E © Addison-Wesley 2009
10
计算机图形学讲义－10
Vanishing Points
• Parallel lines (not parallel to the projection plan) on the object converge at a single point in the projection (the vanishing point) • Drawing simple perspectives by hand uses these vanishing point(s)
计算机图形学讲义－10
Classical Viewing
Each classical view is determined by the specific relationship between the objects and viewer.
计算机图形学讲义－10
Orthographic Projections
Angel: Interactive Computer Graphics 5E © Addison-Wesley 2009
12
计算机图形学讲义－10
Two-Point Perspective
• On principal direction parallel to projection plane • Two vanishing points for cube
计算机图形学讲义－10
Classical and Computer Viewing
• • • • • Classical Viewing Orthographic Projections Axonometric Projections Oblique Projections Perspective Viewing
计算机图形学讲义－10
Oblique Projections
(a) Construction of oblique view projection; (b) top view; (c) side view.
计算机图形学讲义－10
Perspective Projection
• Projectors coverge at center of projection
– It applies the specified projection – orthographic or perspective – to the vertices and puts objects within the specified clipping volume in a normalized clipping volume. • Default camera in OpenGL – the camera is at the origin, – pointing to the negative zdirection, – orthographic view, – Clipping volume centered at the origin, of side length 2.
Angel: Interactive Computer Graphics 5E © Addison-Wesley 2009
15
计算机图形学讲义－10
Viewing with a Computer
• Viewing consists of two fundamental operations. • 1st we must position the camera.