{"id":293,"date":"2018-07-21T05:12:50","date_gmt":"2018-07-21T05:12:50","guid":{"rendered":"http:\/\/csp06.epgpbooks.inflibnet.ac.in\/?post_type=chapter&#038;p=293"},"modified":"2018-12-27T05:41:59","modified_gmt":"2018-12-27T05:41:59","slug":"3d-viewing-projection-transformations","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/csp06\/chapter\/3d-viewing-projection-transformations\/","title":{"rendered":"3D Viewing (Projection Transformations)"},"content":{"raw":"<div><span style=\"float: right\"><a href=\"https:\/\/youtu.be\/Bb8XTNkn7-8\" target=\"_blank\" rel=\"noopener\"><img src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"epgp books\" width=\"75px\" height=\"75px;\" \/><\/a>\r\n<\/span><\/div>\r\n<div>\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n<strong>Objectives:<\/strong>\r\n<ul>\r\n \t<li>To Understand the Projection transformations in 3D<\/li>\r\n<\/ul>\r\n&nbsp;\r\n\r\n<strong>Discussion:<\/strong>\r\n\r\n&nbsp;\r\n\r\n<strong>Parallel Projections:<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">As discussed in the previous module (Module-15), parallel projections are obtained, when objects are projected along lines that are parallel to each other. If the lines of projection are <em>perpendicular<\/em> to the plane of projection, then we get <strong><em>orthographic<\/em><\/strong> projections, otherwise we get <strong><em>oblique<\/em><\/strong> projections.Shown in the figure below are Orthographic projections.<\/p>\r\n&nbsp;\r\n\r\n<img class=\"size-full wp-image-295 aligncenter\" src=\"http:\/\/csp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/52\/2018\/07\/1-207.png\" alt=\"\" width=\"400\" height=\"176\" \/>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">Figure below shows an object projected along lines which make any angle other than 90\u00b0 with view plane. These are <strong>oblique projections<\/strong>.<\/p>\r\n\r\n<\/div>\r\n<img class=\"size-full wp-image-297 aligncenter\" src=\"http:\/\/csp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/52\/2018\/07\/1-208.png\" alt=\"\" width=\"427\" height=\"229\" \/>\r\n<div>\r\n\r\n&nbsp;\r\n\r\n<strong>Orthographic parallel projections:<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">Here a 3D point (x,y,z) is projected as (x,y) on to a view planeas shown.Generally the view plane is assumed to be placed in the XY plane of the viewing coordinate system (whose eq. is Z=0). The default projection is orthographic projection. The shape of the <em>view volume<\/em> is a rectangular parallelepiped as shown in the figure below.<\/p>\r\n&nbsp;\r\n\r\n<img class=\"size-full wp-image-298 aligncenter\" src=\"http:\/\/csp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/52\/2018\/07\/1-209.png\" alt=\"\" width=\"588\" height=\"224\" \/>\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n<strong>Axonometric orthographic projections:<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">The projection plane is aligned so that it intersects each coordinate axes in which the object is defined (principal axes) at the same distance from the origin.All the three principal axes are foreshortened equally.In other words,by aligning the viewplane normal vector along one of the principle diagonals of the cube we get isometric projections of the cube as shown in the figure below.<\/p>\r\n\r\n<\/div>\r\n<img class=\"size-full wp-image-299 aligncenter\" src=\"http:\/\/csp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/52\/2018\/07\/1-210.png\" alt=\"\" width=\"381\" height=\"247\" \/>\r\n<div>\r\n\r\n&nbsp;\r\n\r\n<strong>Oblique parallel projection:<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">When the lines of projection make an angle other than 90\u00b0with the view plane, we get oblique projections. Let\u2019s assume that a point P(x,y,z) is tobe projected onto the viewplane positioned at <em>XY<\/em> plane of the VCS. The orthographic projection coordinates of the point P(x,y,z) on the view plane are (x,y), since z=0 on the view plane. Let <em>\u03b1<\/em> be the angle of projection, and the oblique projection coordinates on the view plane are say (<em>x<\/em><em>p<\/em>,<em>y<\/em><em>p<\/em>). Consider an imaginary line <em>L <\/em>connecting the orthogonal projection coordinates with the oblique projection coordinates as shown in the figure below. Let the line <em>L<\/em>make an angle \u00f8 with the horizontal \/ X-axis of the view plane.<\/p>\r\n<img class=\"size-full wp-image-300 aligncenter\" src=\"http:\/\/csp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/52\/2018\/07\/1-211.png\" alt=\"\" width=\"255\" height=\"248\" \/>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">The line connecting P(x,y,z) and oblique projection coordinates (<em>x<\/em><em>p<\/em>,<em>y<\/em><em>p<\/em>) is the oblique line of projection.The line connecting P(x,y,z) and P(<em>x<\/em>,<em>y<\/em>) is the orthogonal projection line. The <em>cosine<\/em>,<em> sine <\/em>of the angle \u00f8, in the triangle formed by the line<em> L <\/em>and the horizontal (<em>X<\/em>-axis) is given below.<\/p>\r\n&nbsp;\r\n\r\n<img class=\"size-full wp-image-301 aligncenter\" src=\"http:\/\/csp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/52\/2018\/07\/1-212.png\" alt=\"\" width=\"664\" height=\"197\" \/>\r\n\r\n&nbsp;\r\n\r\n<\/div>\r\n<div>\r\n\r\n<img class=\"size-full wp-image-302 aligncenter\" src=\"http:\/\/csp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/52\/2018\/07\/1-213.png\" alt=\"\" width=\"633\" height=\"257\" \/>\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">The effect of this projection matrix is to shear planes of constant <em>z<\/em>. The larger the z-value of a face \/ plane of an object, the more it gets sheared.An <em>orthographi<\/em>c projection is obtained when <em>L<\/em>1=0.In fact the effect of the projection matrix is to <em>shear<\/em> planes of constant <em>Z<\/em> and project them on to the view plane.The angle \u00f8 is generally fixed at 30\u00b0 or 60\u00b0.<\/p>\r\n&nbsp;\r\n\r\n<\/div>\r\n<img class=\"size-full wp-image-303 aligncenter\" src=\"http:\/\/csp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/52\/2018\/07\/1-214.png\" alt=\"\" width=\"686\" height=\"330\" \/>\r\n<div>\r\n\r\n<strong>\u00a0 \u00a0Perspective projections:<\/strong>\r\n\r\n&nbsp;\r\n\r\nThese projections are more realistic.\r\n<ul>\r\n \t<li>Visual effect is similar to human visual system.<\/li>\r\n \t<li>Has<em>\u2018perspective foreshortening\u2019<\/em>.<\/li>\r\n \t<li>Size of object varies inversely with distance from the center of projection.<\/li>\r\n \t<li>Angles only remain intact for faces parallel to projection plane<\/li>\r\n<\/ul>\r\n<\/div>\r\n<img class=\"size-full wp-image-304 aligncenter\" src=\"http:\/\/csp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/52\/2018\/07\/1-215.png\" alt=\"\" width=\"707\" height=\"606\" \/>\r\n<div>\r\n\r\n<img class=\"size-full wp-image-305 aligncenter\" src=\"http:\/\/csp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/52\/2018\/07\/1-216.png\" alt=\"\" width=\"643\" height=\"239\" \/>\r\n\r\n<\/div>\r\n<div><\/div>\r\n<div>\r\n\r\n<img class=\"size-full wp-image-306 aligncenter\" src=\"http:\/\/csp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/52\/2018\/07\/1-217.png\" alt=\"\" width=\"704\" height=\"545\" \/>\r\n\r\n<\/div>\r\n&nbsp;\r\n<div>\r\n\r\n<img class=\"size-full wp-image-307 aligncenter\" src=\"http:\/\/csp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/52\/2018\/07\/1-218.png\" alt=\"\" width=\"689\" height=\"276\" \/>\r\n\r\n<\/div>\r\n<img class=\"size-full wp-image-308 aligncenter\" src=\"http:\/\/csp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/52\/2018\/07\/1-219.png\" alt=\"\" width=\"256\" height=\"224\" \/>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">One-point perspective projection: Only one principle axis has a vanishing point.<\/p>\r\n<p style=\"text-align: justify\">Two-point perspective projection: There are two principle vanishing points.<\/p>\r\n<p style=\"text-align: justify\">Three point perspective Projection: There are three principle vanishing points.<\/p>\r\n&nbsp;\r\n\r\n<img class=\"size-full wp-image-309 aligncenter\" src=\"http:\/\/csp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/52\/2018\/07\/1-220.png\" alt=\"\" width=\"618\" height=\"190\" \/>\r\n\r\n&nbsp;\r\n\r\n<strong>Summary:<\/strong>\r\n<ul>\r\n \t<li>Learnt Parallel projection transformation.<\/li>\r\n \t<li>Learnt orthographic, oblique parallel projections<\/li>\r\n \t<li>Learnt perspective projection transformation<\/li>\r\n<\/ul>\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><strong>you can view video on 3D Viewing (Projection Transformations)<\/strong><\/td>\r\n<td><a href=\"https:\/\/youtu.be\/Bb8XTNkn7-8\" target=\"_blank\" rel=\"noopener\"><img class=\"alignnone wp-image-120\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"\" width=\"36\" height=\"36\" \/><\/a><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>","rendered":"<div><span style=\"float: right\"><a href=\"https:\/\/youtu.be\/Bb8XTNkn7-8\" target=\"_blank\" rel=\"noopener\"><img decoding=\"async\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"epgp books\" width=\"75px\" height=\"75px;\" \/><\/a><br \/>\n<\/span><\/div>\n<div>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Objectives:<\/strong><\/p>\n<ul>\n<li>To Understand the Projection transformations in 3D<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<p><strong>Discussion:<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Parallel Projections:<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">As discussed in the previous module (Module-15), parallel projections are obtained, when objects are projected along lines that are parallel to each other. If the lines of projection are <em>perpendicular<\/em> to the plane of projection, then we get <strong><em>orthographic<\/em><\/strong> projections, otherwise we get <strong><em>oblique<\/em><\/strong> projections.Shown in the figure below are Orthographic projections.<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-295 aligncenter\" src=\"http:\/\/csp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/52\/2018\/07\/1-207.png\" alt=\"\" width=\"400\" height=\"176\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-207.png 400w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-207-300x132.png 300w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-207-65x29.png 65w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-207-225x99.png 225w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-207-350x154.png 350w\" sizes=\"auto, (max-width: 400px) 100vw, 400px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Figure below shows an object projected along lines which make any angle other than 90\u00b0 with view plane. These are <strong>oblique projections<\/strong>.<\/p>\n<\/div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-297 aligncenter\" src=\"http:\/\/csp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/52\/2018\/07\/1-208.png\" alt=\"\" width=\"427\" height=\"229\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-208.png 427w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-208-300x161.png 300w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-208-65x35.png 65w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-208-225x121.png 225w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-208-350x188.png 350w\" sizes=\"auto, (max-width: 427px) 100vw, 427px\" \/><\/p>\n<div>\n<p>&nbsp;<\/p>\n<p><strong>Orthographic parallel projections:<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Here a 3D point (x,y,z) is projected as (x,y) on to a view planeas shown.Generally the view plane is assumed to be placed in the XY plane of the viewing coordinate system (whose eq. is Z=0). The default projection is orthographic projection. The shape of the <em>view volume<\/em> is a rectangular parallelepiped as shown in the figure below.<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-298 aligncenter\" src=\"http:\/\/csp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/52\/2018\/07\/1-209.png\" alt=\"\" width=\"588\" height=\"224\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-209.png 588w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-209-300x114.png 300w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-209-65x25.png 65w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-209-225x86.png 225w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-209-350x133.png 350w\" sizes=\"auto, (max-width: 588px) 100vw, 588px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Axonometric orthographic projections:<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">The projection plane is aligned so that it intersects each coordinate axes in which the object is defined (principal axes) at the same distance from the origin.All the three principal axes are foreshortened equally.In other words,by aligning the viewplane normal vector along one of the principle diagonals of the cube we get isometric projections of the cube as shown in the figure below.<\/p>\n<\/div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-299 aligncenter\" src=\"http:\/\/csp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/52\/2018\/07\/1-210.png\" alt=\"\" width=\"381\" height=\"247\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-210.png 381w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-210-300x194.png 300w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-210-65x42.png 65w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-210-225x146.png 225w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-210-350x227.png 350w\" sizes=\"auto, (max-width: 381px) 100vw, 381px\" \/><\/p>\n<div>\n<p>&nbsp;<\/p>\n<p><strong>Oblique parallel projection:<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">When the lines of projection make an angle other than 90\u00b0with the view plane, we get oblique projections. Let\u2019s assume that a point P(x,y,z) is tobe projected onto the viewplane positioned at <em>XY<\/em> plane of the VCS. The orthographic projection coordinates of the point P(x,y,z) on the view plane are (x,y), since z=0 on the view plane. Let <em>\u03b1<\/em> be the angle of projection, and the oblique projection coordinates on the view plane are say (<em>x<\/em><em>p<\/em>,<em>y<\/em><em>p<\/em>). Consider an imaginary line <em>L <\/em>connecting the orthogonal projection coordinates with the oblique projection coordinates as shown in the figure below. Let the line <em>L<\/em>make an angle \u00f8 with the horizontal \/ X-axis of the view plane.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-300 aligncenter\" src=\"http:\/\/csp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/52\/2018\/07\/1-211.png\" alt=\"\" width=\"255\" height=\"248\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-211.png 255w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-211-65x63.png 65w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-211-225x219.png 225w\" sizes=\"auto, (max-width: 255px) 100vw, 255px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">The line connecting P(x,y,z) and oblique projection coordinates (<em>x<\/em><em>p<\/em>,<em>y<\/em><em>p<\/em>) is the oblique line of projection.The line connecting P(x,y,z) and P(<em>x<\/em>,<em>y<\/em>) is the orthogonal projection line. The <em>cosine<\/em>,<em> sine <\/em>of the angle \u00f8, in the triangle formed by the line<em> L <\/em>and the horizontal (<em>X<\/em>-axis) is given below.<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-301 aligncenter\" src=\"http:\/\/csp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/52\/2018\/07\/1-212.png\" alt=\"\" width=\"664\" height=\"197\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-212.png 664w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-212-300x89.png 300w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-212-65x19.png 65w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-212-225x67.png 225w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-212-350x104.png 350w\" sizes=\"auto, (max-width: 664px) 100vw, 664px\" \/><\/p>\n<p>&nbsp;<\/p>\n<\/div>\n<div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-302 aligncenter\" src=\"http:\/\/csp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/52\/2018\/07\/1-213.png\" alt=\"\" width=\"633\" height=\"257\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-213.png 633w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-213-300x122.png 300w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-213-65x26.png 65w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-213-225x91.png 225w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-213-350x142.png 350w\" sizes=\"auto, (max-width: 633px) 100vw, 633px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">The effect of this projection matrix is to shear planes of constant <em>z<\/em>. The larger the z-value of a face \/ plane of an object, the more it gets sheared.An <em>orthographi<\/em>c projection is obtained when <em>L<\/em>1=0.In fact the effect of the projection matrix is to <em>shear<\/em> planes of constant <em>Z<\/em> and project them on to the view plane.The angle \u00f8 is generally fixed at 30\u00b0 or 60\u00b0.<\/p>\n<p>&nbsp;<\/p>\n<\/div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-303 aligncenter\" src=\"http:\/\/csp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/52\/2018\/07\/1-214.png\" alt=\"\" width=\"686\" height=\"330\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-214.png 686w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-214-300x144.png 300w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-214-65x31.png 65w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-214-225x108.png 225w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-214-350x168.png 350w\" sizes=\"auto, (max-width: 686px) 100vw, 686px\" \/><\/p>\n<div>\n<p><strong>\u00a0 \u00a0Perspective projections:<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>These projections are more realistic.<\/p>\n<ul>\n<li>Visual effect is similar to human visual system.<\/li>\n<li>Has<em>\u2018perspective foreshortening\u2019<\/em>.<\/li>\n<li>Size of object varies inversely with distance from the center of projection.<\/li>\n<li>Angles only remain intact for faces parallel to projection plane<\/li>\n<\/ul>\n<\/div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-304 aligncenter\" src=\"http:\/\/csp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/52\/2018\/07\/1-215.png\" alt=\"\" width=\"707\" height=\"606\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-215.png 707w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-215-300x257.png 300w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-215-65x56.png 65w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-215-225x193.png 225w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-215-350x300.png 350w\" sizes=\"auto, (max-width: 707px) 100vw, 707px\" \/><\/p>\n<div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-305 aligncenter\" src=\"http:\/\/csp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/52\/2018\/07\/1-216.png\" alt=\"\" width=\"643\" height=\"239\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-216.png 643w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-216-300x112.png 300w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-216-65x24.png 65w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-216-225x84.png 225w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-216-350x130.png 350w\" sizes=\"auto, (max-width: 643px) 100vw, 643px\" \/><\/p>\n<\/div>\n<div><\/div>\n<div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-306 aligncenter\" src=\"http:\/\/csp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/52\/2018\/07\/1-217.png\" alt=\"\" width=\"704\" height=\"545\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-217.png 704w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-217-300x232.png 300w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-217-65x50.png 65w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-217-225x174.png 225w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-217-350x271.png 350w\" sizes=\"auto, (max-width: 704px) 100vw, 704px\" \/><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-307 aligncenter\" src=\"http:\/\/csp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/52\/2018\/07\/1-218.png\" alt=\"\" width=\"689\" height=\"276\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-218.png 689w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-218-300x120.png 300w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-218-65x26.png 65w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-218-225x90.png 225w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-218-350x140.png 350w\" sizes=\"auto, (max-width: 689px) 100vw, 689px\" \/><\/p>\n<\/div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-308 aligncenter\" src=\"http:\/\/csp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/52\/2018\/07\/1-219.png\" alt=\"\" width=\"256\" height=\"224\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-219.png 256w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-219-65x57.png 65w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-219-225x197.png 225w\" sizes=\"auto, (max-width: 256px) 100vw, 256px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">One-point perspective projection: Only one principle axis has a vanishing point.<\/p>\n<p style=\"text-align: justify\">Two-point perspective projection: There are two principle vanishing points.<\/p>\n<p style=\"text-align: justify\">Three point perspective Projection: There are three principle vanishing points.<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-309 aligncenter\" src=\"http:\/\/csp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/52\/2018\/07\/1-220.png\" alt=\"\" width=\"618\" height=\"190\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-220.png 618w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-220-300x92.png 300w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-220-65x20.png 65w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-220-225x69.png 225w, https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-content\/uploads\/sites\/52\/2018\/07\/1-220-350x108.png 350w\" sizes=\"auto, (max-width: 618px) 100vw, 618px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Summary:<\/strong><\/p>\n<ul>\n<li>Learnt Parallel projection transformation.<\/li>\n<li>Learnt orthographic, oblique parallel projections<\/li>\n<li>Learnt perspective projection transformation<\/li>\n<\/ul>\n<table>\n<tbody>\n<tr>\n<td><strong>you can view video on 3D Viewing (Projection Transformations)<\/strong><\/td>\n<td><a href=\"https:\/\/youtu.be\/Bb8XTNkn7-8\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-120\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"\" width=\"36\" height=\"36\" \/><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"author":3,"menu_order":16,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":["dr-t-raghuveera"],"pb_section_license":""},"chapter-type":[],"contributor":[59],"license":[],"class_list":["post-293","chapter","type-chapter","status-publish","hentry","contributor-dr-t-raghuveera"],"part":3,"_links":{"self":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-json\/pressbooks\/v2\/chapters\/293","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-json\/wp\/v2\/users\/3"}],"version-history":[{"count":7,"href":"https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-json\/pressbooks\/v2\/chapters\/293\/revisions"}],"predecessor-version":[{"id":627,"href":"https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-json\/pressbooks\/v2\/chapters\/293\/revisions\/627"}],"part":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-json\/pressbooks\/v2\/chapters\/293\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-json\/wp\/v2\/media?parent=293"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-json\/pressbooks\/v2\/chapter-type?post=293"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-json\/wp\/v2\/contributor?post=293"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/csp06\/wp-json\/wp\/v2\/license?post=293"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}