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Cos.htm

Cos.htm 3.5 KB
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  1. <html>
    2. 

  2. <head>
    3. 

  3. <title>Blitz3D Docs</title>
    4. 

  4. <link rel=stylesheet href=../css/commands.css type=text/css>
    5. 

  5. </head>
    6. 

  6. <body>
    7. 

  7. <h1>Cos# ( degrees# )</h1>
    8. 

  8. <h1>Parameters</h1>
    9. 

  9. <table>
    10. 

  10. <tr>
    11. 

  11. <td>
    12. 

  12. degrees# = angle in degrees.
    13. 

  13. </td>
    14. 

  14. </tr>
    15. 

  15. </table>
    16. 

  16. <h1>Description</h1>
    17. 

  17. <table>
    18. 

  18. <tr>
    19. 

  19. <td>
    20. 

  20. For angles between 0 and 90 degrees this is defined by the sides of a right triangle. The cosine is the side adjacent to the angle divided by the hypotenuse.

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    21. 

  21. 
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    22. 

  22. Outside of 0 to 90 the definition uses a circle with radius=1. The angle is placed at the center of the circle, with one side on the positive x-axis. The other side hits the circle at some point. The x coordinate of this point is the cosine of the angle.

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    23. 

  23. 
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    24. 

  24. The positive y-axis corresonds to +90 degrees. This is a common source of confusion in Blitz. With screen coordinates ( pixels ) the y-axis points downward. But in the 3d world the y-axis typically points upward.

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    25. 

  25. 
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    26. 

  26. Another possible snag is the size of the angle. In principle, the cosine function repeats every 360 degrees. So Cos(-360), Cos(0), Cos(360), Cos(720) etc. should all be exactly the same. But in practice the accuracy decreases as the angle gets farther away from zero.

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    27. 

  27. 
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    28. 

  28. 
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    29. 

  29. See also ASin, Cos, ACos, Tan, Atan, ATan2
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  30. </td>
    31. 

  31. </tr>
    32. 

  32. </table>
    33. 

  33. <h1><a href=../2d_examples/Cos.bb>Example</a></h1>
    34. 

  34. <table>
    35. 

  35. <tr>
    36. 

  36. <td>
    37. 

  37. ; Sin / Cos / Tan example.
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    38. 

  38. 
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    39. 

  39. ; Left/Right arrow keys change angle. Escape quits.
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    40. 

  40. 
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    41. 

  41. Const width = 640, height = 480
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    42. 

  42. Const radius# = .2 * height
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    43. 

  43. Const KEY_ESC = 1, KEY_LEFT = 203, KEY_RIGHT = 205 
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    44. 

  44. 
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    45. 

  45. Graphics width, height
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    46. 

  46. SetBuffer BackBuffer( )
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    47. 

  47. Origin width / 3, height / 2
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    48. 

  48. 
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    49. 

  49. angle# = 0.0
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    50. 

  50. 
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    51. 

  51. While Not KeyDown( KEY_ESC )
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    52. 

  52. 
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    53. 

  53. ; NOTE: It is usually best to avoid very large angles.
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    54. 

  54. ;       The 'If angle...' lines show one way to do this.
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    55. 

  55. ;		Mod is another possibility. 
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    56. 

  56. 
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    57. 

  57. If KeyDown( KEY_LEFT ) Then angle = angle - .5
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    58. 

  58. ;	If angle < 0.0 Then angle = angle + 360
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    59. 

  59. 
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    60. 

  60. If KeyDown( KEY_RIGHT ) Then angle = angle + .5
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    61. 

  61. ;	If angle >= 360.0 Then angle = angle - 360
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    62. 

  62. 
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    63. 

  63. Cls
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    64. 

  64. 
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    65. 

  65. Color 80, 80, 0		; pale yellow circle
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    66. 

  66. Oval -radius, -radius, 2 * radius, 2 * radius, False
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    67. 

  67. 
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    68. 

  68. For a# = 0.0 To Abs( angle Mod 360 ) Step .5
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    69. 

  69. 
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    70. 

  70. x# = radius * Cos( a )	; (x,y) is a point on the circle
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    71. 

  71. y# = radius * Sin( a )	; corresponding to angle a.
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    72. 

  72. 
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    73. 

  73. If ( angle Mod 360 < 0 ) Then y = -y	; reverse for negative angle		
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    74. 

  74. WritePixel x, y, $ffff00		; bright yellow
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    75. 

  75. 
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    76. 

  76. Next
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    77. 

  77. 
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    78. 

  78. Color 255, 255, 0		; yellow
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    79. 

  79. Line 0, 0, radius * Cos( angle ), radius * Sin( angle ) 
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    80. 

  80. 
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    81. 

  81. Color 0, 255, 0			; green
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    82. 

  82. Line 0, 0, radius * Cos( angle ), 0
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    83. 

  83. Text radius * 1.5,  10, "Cos( angle ) = " + Cos( angle )
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    84. 

  84. 
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    85. 

  85. Color 255, 0, 0			; red
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    86. 

  86. Line radius * Cos( angle ), 0, radius * Cos( angle ), radius * Sin( angle ) 	
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    87. 

  87. Text radius * 1.5, -10, "Sin( angle ) = " + Sin( angle )
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    88. 

  88. 
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    89. 

  89. Color 255, 255, 255
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    90. 

  90. Text radius * 1.5, -30, "     angle =   " + angle
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    91. 

  91. Text radius * 1.5,  30, "Tan( angle ) = " + Tan( angle ) 
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    92. 

  92. 
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    93. 

  93. Flip
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    94. 

  94. 
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    95. 

  95. Wend
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  96. 
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    97. 

  97. End
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  98. </td>
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  99. </tr>
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  100. </table>
    101. 

  101. <br>
    102. 

  102. <a target=_top href=../index.htm>Index</a><br>
    103. 

  103. <br>
    104. 

  104. Click <a href=http://www.blitzbasic.co.nz/b3ddocs/command.php?name=Cos&ref=comments target=_blank>here</a> to view the latest version of this page online</body>
    105. 

  105. </html>
    106.