Basic Maple Plots - Points and SurfacesBegin by loading the plots package (place cursor at the end of the line below and hit Enter)Change the colon at the end of the line to a semicolon and again hit Enter. Notice the difference in output. with(plots):Part A - Plotting PointsPlot the point 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 using a three-dimensional rectangular coordinate system. Starting from the origin (0, 0, 0), we can reach the point (1, 2, 3) by moving 1 unit along the x-axis, by moving 2 units parallel with the y-axis , and then by moving 3 units parallel with the z-axis. Plot these paths from the origin (0, 0, 0) to the point (1, 2, 3). To create this plot, Figure 1B, we use the Maple pointplot3d function in two ways. Here are the commands and the resulting plot. The second command below saves the output of the pointplot3d command under the name p1. The next three commands save the graphic data for the plot of line segments between the points ( 0, 0, 0) and (1, 0, 0), (1, 0, 0) and (1, 2, 0), and (1, 2, 0) and (1, 2, 3). The display command plots the result of the four previous commands. First a point plot where we end the Maple command with a semicolon, which causes Maple to display the output.pointplot3d([1,2,3], color=blue, symbol=solidsphere, axes=normal, labels=[x,y,z], symbolsize=18, title="Figure 1A: Plotting the Point (1, 2, 3)");
A second example of a pointplot where we plot two points; 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Note that we create a list of points using the curly brackets {...}.pointplot3d({[1,2,3],[1,1,-3]}, color=green, symbol=solidsphere, axes=normal, labels=[x,y,z], symbolsize=25, title="Figure 1B: Plotting the Points (1, 2, 3) and (1, 1, -3");Now we create several plots but suppress the output by ending the lines with a colon.p1 := pointplot3d([1,2,3], color=black, symbol=solidsphere, symbolsize=28):p2 := pointplot3d({[0,0,0],[1,0,0]}, color=red, style=LINE, thickness=2):p3 := pointplot3d({[1,0,0],[1,2,0]}, color=green, style=LINE, thickness=2):p4 := pointplot3d({[1,2,0],[1,2,3]}, color=blue, style=LINE, thickness=2):
We use pointplot3d to plot a single point (p1). In this case, the first argument contains the coordinates of P written as a list using bookend brackets, [1, 2, 3]. The remaining arguments have the syntax, option=value. We also use pointplot3d to draw line segments p2, p3, and p4. In this case, the first argument contains a set of two points. The option style=LINE is used to draw a line segment joining these points. The colon at the end of the assignments for the plots p1, p2, p3, p4 tells Maple not to display the plot data structures. The Maple display function, displays all four plots on the same set of axes. Note the use of the semi-colon ; at the end of this command. In displaying graphs you should always use the axes, labels, and scaling options. The scaling=CONSTRAINED option forces the same length scale to be used on all three axes. display3d({p1,p2,p3,p4}, axes=NORMAL, labels=["x","y","z"], scaling=CONSTRAINED, title="Figure 1C: Plotting the Point (1, 2, 3)");Part B - Plotting SurfacesWe use the command implicitplot3d to plot surfaces in three-space when we don't solve for a dependent variable (usually z).A sphere with center at the origin and a radius of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtc3FydEdGJDYjLUYjNiZGKy1JI21uR0YkNiZRIzE0RicvJSVib2xkR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSVib2xkRicvJStmb250d2VpZ2h0R0Y9RisvRjxRJ25vcm1hbEYnRitGQA==, having the equation 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implicitplot3d(x^2+y^2+z^2=14,x=-7..7,y=-7..7,z=-7..7, grid=[20,20,20], axes=boxed);The plane x=3.implicitplot3d(x=3,x=-5..5,y=-5..5,z=-5..5, axes=normal, style=surface, transparency=0.5, grid=[20,20,20]);A sphere not centered at the origin. Show that 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 is the equation of a sphere. Find its center and radius. Then plot.The trick is to complete the square on the x, y, and z terms: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 = 0 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 = 0 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 = 0 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The center is (LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2I1EhRictRiM2JS1JI21vR0YkNi1RKiZ1bWludXMwO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOi8lKXN0cmV0Y2h5R0Y6LyUqc3ltbWV0cmljR0Y6LyUobGFyZ2VvcEdGOi8lLm1vdmFibGVsaW1pdHNHRjovJSdhY2NlbnRHRjovJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZJLUkjbW5HRiQ2JFEiMkYnRjVGNS1GMjYtUSIsRidGNUY4L0Y8USV0cnVlRidGPUY/RkFGQ0ZFRkcvRktRLDAuMzMzMzMzM2VtRictRk02JFEiM0YnRjVGUC1GIzYlRjEtRk02JFEiMUYnRjVGNUYrRjU=) and the radius is LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtc3FydEdGJDYjLUkjbW5HRiQ2JFEiOEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0YrRjY=.implicitplot3d(x^2+y^2+z^2+4*x-6*y+2*z+6=0, x=-5..5, y=-2..8, z=-5..5, axes=normal, grid=[20, 20, 20]);********Important Problem for Maple HW #1********A plane and a point in the plane plotted together on the same axesplane1:=implicitplot3d(z=-2,x=-5..5,y=-5..5,z=-5..5, axes=normal, style=surface, grid=[20,20,20]):
point1:=pointplot3d([3,2,-2],color=blue, symbol=solidsphere, symbolsize=20):
display3d(plane1, point1);END