ssrs barcode font download Torus and MoebiusStrip are also available in the kernel function ExampleData. in Software

Generating QR Code in Software Torus and MoebiusStrip are also available in the kernel function ExampleData.

Torus and MoebiusStrip are also available in the kernel function ExampleData.
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Cylinder[r, h, n] draws a cylinder with radius r and half height h using n polygons. Sphere[r, n, m] draws a sphere of radius r using n(m 2)+ 2 polygons. Cone[r, h, n] draws a cone with radius r and half height h using n polygons. Torus[r1, r2, n, m]draws a torus with radii r1 and r2 using an n m mesh. MoebiusStrip[r1, r2, n] draws a Moebius strip with radii r1 and r2 using 2n polygons. Helix[r, h, m, n] draws a helix with radius r, half height h, and m turns using an n m mesh. DoubleHelix[r, h, m, n] draws a double helix with radius r, half height h, and m turns using an n m mesh.
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If the parameters are omitted, e.g., Cone[] Mathematica s defaults are used. The default values are , Cylinder[1, 1, 20] Sphere[1, 20, 15] Cone[1, 1, 20] Torus[1, .5, 20, 10] MoebiusStrip[1, .5, 20] Helix[1, .5, 2, 20] DoubleHelix[1, .5, 2, 20]
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EXAMPLE 24
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Graphics` Graphics3D[Cylinder[]] Graphics3D[Sphere[]] Graphics3D[Cone[]] Graphics3D[Torus[]] Graphics3D[MoebiusStrip[]] Graphics3D[Helix[]] Graphics3D[DoubleHelix[]]
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WireFrame[object] shows all polygons used in the construction of object as transparent. It may be used on any Graphics3D object that contains the primitives Polygon, Line, and Point. Opacity[a]specifies the degree of transparency of a graphics object. The value of a must be between 0 and 1, with 0 representing perfect transparency and 1 representing complete opaqueness.
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The Opacity directive should be placed within the Graphics3D directive as shown in the following example.
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Graphics` object = Torus[ ]; Graphics3D[object] Graphics3D[{Opacity[.3], object}] WireFrame[object]
There are three commands in Graphics` that provide transformations in space:
RotateShape[object, e, p, x] rotates object using the Euler angles1 , , and . TranslateShape[object, {x, y, z}] translates object by the vector {x, y, z}]. AffineShape[object, {xscale, yscale, zscale}] scales the x-, y-, and z-coordinates by xscale, yscale, and zscale, respectively.
EXAMPLE 26
Graphics` object = Graphics3D[Cone[]] RotateShape[object, 0, o/2, 0] RotateShape[object, 0, o/2, o/2]
1 Euler angles are a way of describing transformations in R3 by performing three rotations in a specified sequence. First we make a rotation about the z-axis. Then we perform a rotation about the new y-axis. Finally, we perform a rotation about the (new) z-axis obtained from this rotation.
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Show[object, TranslateShape[object, {1, 2, 3}]] shrunkenobject = Af neShape[object, {.5, .5, .5}]; Show[object, TranslateShape[shrunkenobject, {1, 2, 3}]]
SOLVED PROBLEMS
5.24 Draw two cylinders intersecting at right angles.
SOLUTION
Graphics` cyl1 = Graphics3D[Cylinder[1, 5, 20]]; cyl2 = Graphics3D[RotateShape[Cylinder[1, 5, 20], 0, o/2, 0]]; Show[cyl1, cyl2]
Three-Dimensional Graphics
5.25 Construct a cylinder inscribed in a sphere of radius 1.
SOLUTION 1
Since the sphere has radius 1, we use the default parameters. In order for the cylinder to be inscribed in the sphere, r (radius) and h (half height) must satisfy r 2 + h 2 = 1 . We choose r = 1 / 2 and h = 3 / 2 . In order for the cylinder to be visible, we draw the sphere as a wire frame. Graphics` sphere = WireFrame[Graphics3D[{Opacity[0.5], Sphere [{0, 0, 0}, 1]}]]; 3 , 0, 0, 3 , 1 ; cylinder = Graphics3D Cylinder 0, 0, 2 2 2 Show[sphere, cylinder, Boxed False]
SOLUTION 2
Using the graphics Directive Opacity, we can make the sphere semitransparent so the cylinder is visible through the sphere. sphere = Graphics3D[{Opacity[0.5], Sphere[ ]}] ; 3 , 0, 0, 3 cylinder = Graphics3D Cylinder 0, 0, 2 2 Show[sphere, cylinder, Boxed False]
, 1 ; 2
Three-Dimensional Graphics
5.26 Draw two interlocking tori of default dimension (r1 = 1, r2 = 0.5).
SOLUTION
The second torus must be rotated 90 and translated one unit so that they interlock without intersecting. Graphics` torus1 = Graphics3D[Torus[]]; torus2 = Graphics3D[TranslateShape[RotateShape[Torus[], 0, o/2, o/2], {0, .5, 0}]]; Show[torus1, torus2, ViewPoint {1.75, 2.8, 0.75}, Boxed False]
5.27 Construct an animation showing a helix revolving about the z-axis.
SOLUTION
We use a default helix, helix[]. The helix makes one complete revolution as the Euler angle, , varies from 0 to 2 . Graphics` Animate[Graphics3D[RotateShape[Helix[], e, 0, 0], Boxed False], {e, 0, 2 o}]
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