Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
General-purpose computing on graphics processing units wikipedia , lookup
Free and open-source graphics device driver wikipedia , lookup
BSAVE (bitmap format) wikipedia , lookup
Waveform graphics wikipedia , lookup
Framebuffer wikipedia , lookup
Apple II graphics wikipedia , lookup
InfiniteReality wikipedia , lookup
Tektronix 4010 wikipedia , lookup
2. Principles of Mathematica 462 2.9.2 Two-Dimensional Graphics Elements Point {x, y}] point at position x, y Line {{x1 , y1 }, {x2 , y2 }, ... }] line through the points {x1 , y1 }, {x2 , y2 }, ... Rectangle {xmin, ymin}, {xmax, ymax}] filled rectangle Polygon {{x1 , y1 }, {x2 , y2 }, ... }] filled polygon with the specified list of corners Circle {x, y}, r] Disk {x, y}, r] circle with radius r centered at x, y filled disk with radius r centered at x, y Raster {{a11 , a12 , ... }, {a21 , ... }, ... }] rectangular array of gray levels between 0 and 1 Text expr, {x, y}] the text of expr, centered at x, y (see Section 2.9.16) Basic two-dimensional graphics elements. Here is a line primitive. In 1]:= sawline = LineTable{n, (-1)^n}, {n, 6}]] Out 1]= Line {{1, -1}, {2, 1}, {3, -1}, {4, 1}, {5, -1}, {6, 1}}] This shows the line as a two-dimensional graphics object. In 2]:= sawgraph = Show Graphicssawline] ] Web sample page from The Mathematica Book, Second Edition, by Stephen Wolfram, published by Addison-Wesley Publishing Company (hardcover ISBN 0-201-51502-4; softcover ISBN 0-201-51507-5). To order Mathematica or this book contact Wolfram Research: [email protected]; http://www.wolfram.com/; 1-800-441-6284. 1991 Wolfram Research, Inc. Permission is hereby granted for web users to make one paper copy of this page for their personal use. Further reproduction, or any copying of machine-readable files (including this one) to any server computer, is strictly prohibited. 2.9 The Structure of Graphics and Sound This redisplays the line, with axes added. 463 In 3]:= Show %, Axes -> True ] 1 0.5 2 4 3 5 6 -0.5 -1 You can combine graphics objects that you have created explicitly from graphics primitives with ones that are produced by functions like Plot. This produces an ordinary Mathematica plot. In 4]:= PlotSinPi x], {x, 0, 6}] 1 0.5 1 2 3 4 5 6 3 4 5 6 -0.5 -1 This combines the plot with the sawtooth picture made above. In 5]:= Show%, sawgraph] 1 0.5 1 2 -0.5 -1 You can combine different graphical elements simply by giving them in a list. In two-dimensional graphics, Mathematica will render the elements in exactly the order you give them. Later elements are therefore effectively drawn on top of earlier ones. Web sample page from The Mathematica Book, Second Edition, by Stephen Wolfram, published by Addison-Wesley Publishing Company (hardcover ISBN 0-201-51502-4; softcover ISBN 0-201-51507-5). To order Mathematica or this book contact Wolfram Research: [email protected]; http://www.wolfram.com/; 1-800-441-6284. 1991 Wolfram Research, Inc. Permission is hereby granted for web users to make one paper copy of this page for their personal use. Further reproduction, or any copying of machine-readable files (including this one) to any server computer, is strictly prohibited. 2. Principles of Mathematica 464 Here is a list of two Rectangle graphics elements. In 6]:= {Rectangle{1, -1}, {2, -0.6}], Rectangle{4, .3}, {5, .8}]} Out 6]= {Rectangle {1, -1}, {2, -0.6}], Rectangle {4, 0.3}, {5, 0.8}]} This draws the rectangles on top of the line that was defined above. In 7]:= Show Graphics {sawline, %} ]] The Polygon graphics primitive takes a list of x, y coordinates, corresponding to the corners of a polygon. Mathematica joins the last corner with the first one, and then fills the resulting area. Here are the coordinates of the corners of a regular pentagon. In 8]:= pentagon = Table{Sin2 Pi n/5], Cos2 Pi n/5]}, {n, 5}] 2 Pi 2 Pi 4 Pi 4 Pi Out 8]= {{Sin -------], Cos -------]}, {Sin -------], Cos -------]}, 5 5 5 5 6 Pi 6 Pi 8 Pi 8 Pi {Sin -------], Cos -------]}, {Sin -------], Cos -------]}, {0, 1}} 5 5 5 5 This displays the pentagon. With the default choice of aspect ratio, the pentagon looks somewhat squashed. In 9]:= Show Graphics Polygonpentagon] ] ] Web sample page from The Mathematica Book, Second Edition, by Stephen Wolfram, published by Addison-Wesley Publishing Company (hardcover ISBN 0-201-51502-4; softcover ISBN 0-201-51507-5). To order Mathematica or this book contact Wolfram Research: [email protected]; http://www.wolfram.com/; 1-800-441-6284. 1991 Wolfram Research, Inc. Permission is hereby granted for web users to make one paper copy of this page for their personal use. Further reproduction, or any copying of machine-readable files (including this one) to any server computer, is strictly prohibited. 2.9 The Structure of Graphics and Sound 465 This chooses the aspect ratio so that the shape of the pentagon is preserved. In 10]:= Show%, AspectRatio -> Automatic] Mathematica can handle polygons which fold over themselves. In 11]:= ShowGraphics Circle {x, y}, r] Circle {x, y}, {rx , ry }] Polygon {{-1, -1}, {1, 1}, {1, -1}, {-1, 1}} ] ]] a circle with radius r centered at the point {x, y} an ellipse with semi-axes rx and ry Circle {x, y}, r, {theta1 , theta2 }] a circular arc Circle {x, y}, {rx , ry }, {theta1 , theta2 }] an elliptical arc Disk {x, y}, r], etc. filled disks Circles and disks. Web sample page from The Mathematica Book, Second Edition, by Stephen Wolfram, published by Addison-Wesley Publishing Company (hardcover ISBN 0-201-51502-4; softcover ISBN 0-201-51507-5). To order Mathematica or this book contact Wolfram Research: [email protected]; http://www.wolfram.com/; 1-800-441-6284. 1991 Wolfram Research, Inc. Permission is hereby granted for web users to make one paper copy of this page for their personal use. Further reproduction, or any copying of machine-readable files (including this one) to any server computer, is strictly prohibited. 2. Principles of Mathematica 466 This shows two circles with radius 2. Setting the option AspectRatio -> Automatic makes the circles come out with their natural aspect ratio. In 12]:= Show Graphics This shows a sequence of disks with progressively larger semi-axes in the x direction, and progressively smaller ones in the y direction. In 13]:= Show Graphics {Circle{0, 0}, 2], Circle{1, 1}, 2]} ], AspectRatio -> Automatic ] TableDisk{3n, 0}, {n/4, 2-n/4}], {n, 4}] ], AspectRatio -> Automatic ] Mathematica allows you to generate arcs of circles, and segments of ellipses. These objects are specified by starting and finishing angles. Angles are measured counter-clockwise in radians with zero corresponding to the positive x direction. Angle measure always corresponds to circular geometry. This draws a 140 wedge centered at the origin. In 14]:= Show Graphics Disk{0, 0}, 1, {0, 140 Degree}] ], AspectRatio -> Automatic ] Web sample page from The Mathematica Book, Second Edition, by Stephen Wolfram, published by Addison-Wesley Publishing Company (hardcover ISBN 0-201-51502-4; softcover ISBN 0-201-51507-5). To order Mathematica or this book contact Wolfram Research: [email protected]; http://www.wolfram.com/; 1-800-441-6284. 1991 Wolfram Research, Inc. Permission is hereby granted for web users to make one paper copy of this page for their personal use. Further reproduction, or any copying of machine-readable files (including this one) to any server computer, is strictly prohibited. 2.9 The Structure of Graphics and Sound 467 Raster {{a11 , a12 , ... }, {a21 , ... }, ... }] array of gray levels between 0 and 1 Raster array, {{xmin, ymin}, {xmax, ymax}}, {zmin, zmax}] array of gray levels between zmin and zmax drawn in the rectangle defined by {xmin, ymin} and {xmax, ymax} RasterArray {{g11 , g12 , ... }, {g21 , ... }, ... }] rectangular array of cells colored according to the graphics directives gij Raster-based graphics elements. Here is a 4 and 1. 4 array of values between 0 In 15]:= modtab = TableModi, j]/3, {i, 4}, {j, 4}] // N Out 15]= {{0, 0.333333, 0.333333, 0.333333}, {0, 0, 0.666667, 0.666667}, {0, 0.333333, 0, 1.}, {0, 0, 0.333333, 0}} This uses the array of values as gray levels in a raster. In 16]:= Show Graphics Raster%] ] ] Web sample page from The Mathematica Book, Second Edition, by Stephen Wolfram, published by Addison-Wesley Publishing Company (hardcover ISBN 0-201-51502-4; softcover ISBN 0-201-51507-5). To order Mathematica or this book contact Wolfram Research: [email protected]; http://www.wolfram.com/; 1-800-441-6284. 1991 Wolfram Research, Inc. Permission is hereby granted for web users to make one paper copy of this page for their personal use. Further reproduction, or any copying of machine-readable files (including this one) to any server computer, is strictly prohibited. 468 This shows two overlapping copies of the raster. 2. Principles of Mathematica In 17]:= Show Graphics {Rastermodtab, {{0, 0}, {2, 2}}], Rastermodtab, {{1.5, 1.5}, {3, 2}}]} ] ] In the default case, Raster always generates an array of gray cells. As described on page 489, you can use the option ColorFunction to apply a “coloring function” to all the cells. You can also use the graphics primitive RasterArray. While Raster takes an array of values, RasterArray takes an array of Mathematica graphics directives. The directives associated with each cell are taken to determine the color of that cell. Typically the directives are chosen from the set GrayLevel, RGBColor or Hue. By using RGBColor and Hue directives, you can create color rasters using RasterArray. Web sample page from The Mathematica Book, Second Edition, by Stephen Wolfram, published by Addison-Wesley Publishing Company (hardcover ISBN 0-201-51502-4; softcover ISBN 0-201-51507-5). To order Mathematica or this book contact Wolfram Research: [email protected]; http://www.wolfram.com/; 1-800-441-6284. 1991 Wolfram Research, Inc. Permission is hereby granted for web users to make one paper copy of this page for their personal use. Further reproduction, or any copying of machine-readable files (including this one) to any server computer, is strictly prohibited.