 January 19, 2021, 06:24:57 AM

### Author Topic: [bb] Sin() and Cos() demo by Rhodan [ 1+ years ago ]  (Read 738 times)

#### BlitzBot

• Jr. Member
•  • Posts: 1 ##### [bb] Sin() and Cos() demo by Rhodan [ 1+ years ago ]
« on: June 29, 2017, 12:28:42 AM »
Title : Sin() and Cos() demo
Author : Rhodan
Posted : 1+ years ago

Description : Displays X (Sin) and Y(Cos) components and the resulting movement direction and speed as lines on the screen. Heavily commented.

Code :
Code: BlitzBasic
1. [code]
2. ;============================================
3. ;     Demostration of Sin() and Cos()       =
4. ;     (good for ship movement like in)      =
5. ;               ASTEROOIDS!                 =
6. ;============================================
7.
8.
9.
10. Graphics 640,480
11.
12. shipspeed#=0
13. shipangle#=0
14.
15. orig_x#=GraphicsWidth()/2 ; get center of screen for everything
16. orig_y#=GraphicsHeight()/2
17. ship_x#=orig_x#
18. ship_y#=orig_y#
19.
20. SetBuffer BackBuffer()
21.
22. Repeat
23.
24. Cls
25.
26. If KeyDown(200) Then                            ; up arrow
27.
28.         shipspeed#=shipspeed#+1
29.         If shipspeed#>200 Then shipspeed#=200
30.
31. ElseIf KeyDown(208) Then                        ; down arrow
32.
33.         shipspeed#=shipspeed#-1
34.         If shipspeed#<0 Then shipspeed#=0
35.
36. EndIf
37.
38. ;================================================
39. ;                 Ship Angle                    =
40. ; The first thing you have to do is give your   =
41. ; ship a rotation. You rotate in a circle so    =
42. ; you need a number between 0 and 359. Wrap the =
43. ; value by adding or subtracting 360 from it    =
44. ; when it goes out of range. The example below  =
45. ; only steps by 1s so its would work if I just  =
46. ; made it go to 359 if it was less than zero    =
47. ; but, you'll probably be using floats so it    =
48. ; wouldn't work quite right. Better this way    =
49. ;================================================
50.
51. If KeyDown(203) Then                            ; left arrow
52.
53.         shipangle#=shipangle#-1
54.         If shipangle#<0 Then shipangle#=shipangle#+360
55.
56. ElseIf KeyDown(205) Then                        ; right arrow
57.
58.         shipangle#=shipangle#+1
59.         If shipangle#>359 Then shipangle#=shipangle#-360
60.
61. EndIf
62.
63. ; Now that we have a ship angle, we know where its
64. ; pointing. Look at the chart below. If the ship is
65. ; at 45 degrees, it would be pointing down and to
66. ; the left. To move in that direction you need a
67. ; negative change in its X coord and a positive
68. ; change in its Y coord. This is where Sin() and
69. ; Cos() come in. In your windows calculator (in
71. ; scientific mode. Near the lower left side are
72. ; Sin and Cos buttons. Type in 45 then hit the
73. ; Sin button. This will give you the change in
74. ; X you'll need. Now do the same for Cos - which
75. ; is the change in Y. You'll see its the same
76. ; value. Both are about .707. Thats the amount
77. ; you'd have to change each coordinate by to move
78. ; 1 unit of distance at 45 degrees. Try some
79. ; other angles. You'll notice that this chart and
80. ; those numbers disagree about the sign of the
81. ; Sin results. Where this chart shows negative,
82. ; the calculator shows positive etc. Thats
83. ; because computer graphics are the opposite
84. ; in how they number horizontaly. Thats why the
85. ; formula below subtracts Sin and adds Cos.
86. ;
87. ; Anyway, an angle of 45 degrees would need to
88. ; move -.707 in the X sin(45) and +0.707 in the
89. ; y Cos(45) planes. Imagine a little arrow
90. ; from 0,0 to -0.707,0.707. That would be what
91. ; people refer to as a "vector". If you measured
92. ; its length, you'd see it was exactly the same
93. ; length as it would be If it went +1 at 90
94. ; degrees.
95.
96. ; Here's the world according to 2D graphics
97. ;                   180 degrees
98. ;           -x,-y       | -y    +x,-y
99. ;                       |
100. ;                       |
101. ;                       |
102. ;           -x          |          +x
103. ;90 degrees ------------+------------ 270 degrees
104. ;                       |
105. ;                       |
106. ;                       |
107. ;                       |
108. ;           -x,+y       | +y    +x,+y
109.
110. ;                  0/360 Degrees
111.
112.
113.
114.
115. ; Sin() Returns the horizontal component of an angle
116. ; Cos() Returns the vertical component of an angle
117.
118. component_x#=Sin(shipangle#)
119. component_y#=Cos(shipangle#)
120.
121. ; Now that you know how much you need to move in each
122. ; direction, multiply that by the speed of your ship.
123. ; Lets assume you're going speed 10 at 120 degrees.
124.
125. displaced_x#=component_x#*shipspeed# ; 0.866 * 10 = 8.66
126. displaced_y#=component_y#*shipspeed# ; -0.5 * 10 = -5
127.
128.
129. speeddir_x#=orig_x#-displaced_x# ; Now subtract from the ship's X position
130. speeddir_y#=orig_y#+displaced_y# ; and add to the Y position
131.
132. ; Now to show things on the screen.
133.
134. Color 255,255,255
135. Line orig_x#,orig_y#,speeddir_x#,speeddir_y# ; Shows direction and speed of ship
136. Text speeddir_x#,speeddir_y#,"Ship speed: "+Int shipspeed#
137.
138. ; Draw X component size
139. If displaced_x#<0 Then Color 0,0,255 Else Color 255,0,0
140. Line orig_x#,orig_y#,speeddir_x#,orig_y#
141. Color 255,255,255
142. Text speeddir_x#,orig_y#,"DX "+Int (0-displaced_x#) ; Int them, too many numbers flying around =)
143.
144. ; Draw Y component size
145. If displaced_y#>0 Then Color 0,0,255 Else Color 255,0,0
146. Line orig_x#,orig_y#,orig_x#,speeddir_y#
147. Color 255,255,255
148. Text orig_x#,speeddir_y#,"YX "+ Int displaced_y#
149.
150. Color 255,255,255
151. Text 20,GraphicsHeight()-40,"Ship angle: "+shipangle#+" Sin: "+Sin(shipangle#)+" Cos: "+Cos(shipangle#)
152.
153. Flip
154.
155. Until KeyDown(1)
156.
157. End
158.
159.
160.
[/code]

Nicstt(Posted 1+ years ago)

thx for this, finally beginning to understand sin and cos:)

itoleck(Posted 1+ years ago)

Here is the updated code for BlitzMaxRem;============================================;     Demostration of Sin() And Cos()       =;     (good For ship movement like in)      =;               ASTEROOIDS!                 =;============================================EndRemConst ScreenX=800, ScreenY=600Graphics ScreenX,ScreenYshipspeed#=0shipangle#=0orig_x#=ScreenX/2 ' get center of screen For everythingorig_y#=ScreenY/2ship_x#=orig_x#ship_y#=orig_y#RepeatClsIf KeyDown(KEY_UP) Then            ' up arrow   shipspeed#=shipspeed#+1   If shipspeed#>200 Then shipspeed#=200ElseIf KeyDown(KEY_DOWN) Then         ' down arrow   shipspeed#=shipspeed#-1   If shipspeed#<0 Then shipspeed#=0EndIfRem;================================================;                 Ship Angle                    =; The first thing you have To do is give your   =; ship a rotation. You rotate in a circle so    =; you need a number between 0 And 359. Wrap the =; value by adding Or subtracting 360 from it    =; when it goes out of range. The example below  =; only steps by 1s so its would work If I just  =; made it go To 359 If it was less than zero    =; but, you'll probably be using floats so it    =; wouldn't work quite right. Better this way    =;================================================EndRemIf KeyDown(KEY_LEFT) Then            ' Left arrow   shipangle#=shipangle#-1   If shipangle#<0 Then shipangle#=shipangle#+360ElseIf KeyDown(KEY_RIGHT) Then         ' Right arrow   shipangle#=shipangle#+1   If shipangle#>359 Then shipangle#=shipangle#-360EndIfRem; Now that we have a ship angle, we know where its; pointing. Look at the chart below. If the ship is; at 45 degrees, it would be pointing down And To; the left. To move in that direction you need a; negative change in its X coord And a positive; change in its Y coord. This is where Sin() And; Cos() come in. In your windows calculator (in; start menu/programs/accessories), choose; scientific mode. Near the Lower Left side are; Sin And Cos buttons. Type in 45 Then hit the; Sin button. This will give you the change in; X you'll need. Now do the same for Cos - which; is the change in Y. You'll see its the same; value. Both are about .707. Thats the amount; you'd have to change each coordinate by to move; 1 unit of distance at 45 degrees. Try some; other angles. You'll notice that this chart and; those numbers disagree about the sign of the; Sin results. Where this chart shows negative,; the calculator shows positive etc. Thats; because computer Graphics are the opposite; in how they number horizontaly. Thats why the; formula below subtracts Sin And adds Cos.;; Anyway, an angle of 45 degrees would need To; move -.707 in the X Sin(45) And +0.707 in the; y Cos(45) planes. Imagine a little arrow; from 0,0 To -0.707,0.707. That would be what; people refer To as a "vector". If you measured; its length, you'd see it was exactly the same; length as it would be If it went +1 at 90; degrees.; Here's the world according to 2D graphics;                   180 degrees;           -x,-y       | -y    +x,-y;                       |;                       |;                       |;           -x          |          +x;90 degrees ------------+------------ 270 degrees;                       |;                       |;                       |;                       |;           -x,+y       | +y    +x,+y;                  0/360 Degrees; Sin() Returns the horizontal component of an angle; Cos() Returns the vertical component of an angleEndRemcomponent_x#=Sin(shipangle#)component_y#=Cos(shipangle#)Rem; Now that you know how much you need To move in each; direction, multiply that by the speed of your ship.; Lets assume you're going speed 10 at 120 degrees.EndRemdisplaced_x#=component_x#*shipspeed# ' 0.866 * 10 = 8.66 displaced_y#=component_y#*shipspeed# ' -0.5 * 10 = -5speeddir_x#=orig_x#-displaced_x# ' Now subtract from the ship's X positionspeeddir_y#=orig_y#+displaced_y# ' And add To the Y position' Now To show things on the screen.SetColor 255,255,255DrawLine(orig_x#,orig_y#,speeddir_x#,speeddir_y#) ' Shows direction And speed of shipDrawText("Ship speed: "+Int shipspeed#,speeddir_x#,speeddir_y#)' Draw X component sizeIf displaced_x#<0 Then SetColor 0,0,255 Else SetColor 255,0,0DrawLine(orig_x#,orig_y#,speeddir_x#,orig_y#)SetColor 255,255,255DrawText("DX "+Int (0-displaced_x#),speeddir_x#,orig_y#) ' Int them, too many numbers flying around =)' Draw Y component sizeIf displaced_y#>0 Then SetColor 0,0,255 Else SetColor 255,0,0DrawLine(orig_x#,orig_y#,orig_x#,speeddir_y#)SetColor 255,255,255DrawText("YX "+ Int displaced_y#,orig_x#,speeddir_y#)SetColor 255,255,255DrawText("Ship angle: "+shipangle#+" Sin: "+Sin(shipangle#)+" Cos: "+Cos(shipangle#),20,ScreenY-40)FlipUntil KeyDown(KEY_ESCAPE)End