� >HAR-Cube
� Program : HAR-Cube
-�           A simple 3D cube in BBC BASIC
(� Author  : Kevin J Swinton
2 � Version : Acorn A5000.1.00
<%� Date    : Thursday 5th May 1994
F
P
Z#� � � � : � : � " at Line ";�:�
d
n
xN� ------------------------------------------------------------------------
�/�                              MAIN PROGRAM
�N� ------------------------------------------------------------------------
�
�
�� 12+128 : �
�
� �edure_Initialise
� �edure_Cube
�
��
�
�
�N� ------------------------------------------------------------------------

@�         PROCEDURE TO INITIALISE EVERYTHING WE NEED TO KNOW

N� ------------------------------------------------------------------------



"

,� �edure_Initialise

6

@; � *** Place our origin in the middle of the screen ***

J ȑ 640 , 512

T

^9 � *** Dimension all the arrays that we will need ***

hN � array_for_the_3D_points( 8 , 3 ) : � 8 points, each being an X,Y,Z (3D)

rN � array_for_the_2D_points( 8 , 2 ) : � 8 points, each being an X,Y   (2D)

|b � array_for_the_facets( 12 , 4 )    : � 12 facets, each being 3 point references and a colour

�

�I � *** Read all the information we need into our arrays. Firstly, ***

�I � *** read in all our points that make up the cube, and then     ***

�I � *** read in all the facets that join the points together.      ***

�( �edure_Read_Points_Into_Their_Array

�( �edure_Read_Facets_Into_Their_Array

�

�
 BANK = 1

�% �edure_Swap_The_Screen_Banks : �

�% �edure_Swap_The_Screen_Banks : �

�

�= � *** Initialise the rotation of the object in space ***

� X_ROTATION = 0
 Y_ROTATION = 0
 Z_ROTATION = 0

&= � *** Initialise the position of the object in space ***
0= � *** so that it is quite far away from us           ***
: X_POSITION = + 0
D Y_POSITION = + 0
N Z_POSITION = +50
X
b � scale = 1 � 15
l  r = scale * 16
v  g = 96
�  b = 128 + scale * 4
�  � scale , r , g , b
� � scale
�
��
�
�
�N� ------------------------------------------------------------------------
�D�      MAIN PROCEDURE TO CONTROL THE SPINNING CUBE ON THE SCREEN
�N� ------------------------------------------------------------------------
�
�
�� �edure_Cube

 �

     �edure_Rotate_The_Cube
*    �edure_Draw_The_Cube
4$    �edure_Swap_The_Screen_Banks
>
HY    X_ROTATION = X_ROTATION + 1 : � X_ROTATION >= 360 � X_ROTATION = X_ROTATION - 360
RY    Y_ROTATION = Y_ROTATION + 1 : � Y_ROTATION >= 360 � Y_ROTATION = Y_ROTATION - 360
\Y    Z_ROTATION = Z_ROTATION + 1 : � Z_ROTATION >= 360 � Z_ROTATION = Z_ROTATION - 360
f
p � 1 = 2
z
��
�
�
�N� ------------------------------------------------------------------------
�@�        THE PROCEDURE THAT ROTATES THE 8 POINTS OF THE CUBE
�N� ------------------------------------------------------------------------
�
�
�� �edure_Rotate_The_Cube
�
� � point_to_rotate = 1 � 8
�
�J  x_position_of_point = array_for_the_3D_points( point_to_rotate , 1 )
J  y_position_of_point = array_for_the_3D_points( point_to_rotate , 2 )
J  z_position_of_point = array_for_the_3D_points( point_to_rotate , 3 )

$@  � *** Formula for rotating the point around the X axis ***
.i  rotated_y_value = y_position_of_point * �( � X_ROTATION ) - z_position_of_point * �( � X_ROTATION )
8i  rotated_z_value = y_position_of_point * �( � X_ROTATION ) + z_position_of_point * �( � X_ROTATION )
B+  y_position_of_point = rotated_y_value
L+  z_position_of_point = rotated_z_value
V
`@  � *** Formula for rotating the point around the Y axis ***
ji  rotated_x_value = x_position_of_point * �( � Y_ROTATION ) + z_position_of_point * �( � Y_ROTATION )
ti  rotated_z_value = z_position_of_point * �( � Y_ROTATION ) - x_position_of_point * �( � Y_ROTATION )
~+  x_position_of_point = rotated_x_value
�+  z_position_of_point = rotated_z_value
�
�@  � *** Formula for rotating the point around the Z axis ***
�i  rotated_x_value = x_position_of_point * �( � Z_ROTATION ) - y_position_of_point * �( � Z_ROTATION )
�i  rotated_y_value = x_position_of_point * �( � Z_ROTATION ) + y_position_of_point * �( � Z_ROTATION )
�+  x_position_of_point = rotated_x_value
�+  y_position_of_point = rotated_y_value
�
�A  � *** Now we've rotated the object about itself we must ***
�A  � *** position it in space relative to where WE are     ***
�<  x_position_of_point = x_position_of_point + X_POSITION
�<  y_position_of_point = y_position_of_point + Y_POSITION
<  z_position_of_point = z_position_of_point + Z_POSITION


I  � *** Convert from the rotated 3D position into the relevant    ***
I  � *** 2D position. Don't forget that this involves dividing     ***
(I  � *** X and Y by Z, and apllying a perspective factor (eg. 800) ***
2j  array_for_the_2D_points( point_to_rotate , 1 ) = ( 800 * x_position_of_point ) / z_position_of_point
<j  array_for_the_2D_points( point_to_rotate , 2 ) = ( 800 * y_position_of_point ) / z_position_of_point
F
P � point_to_rotate
Z
d�
n
x
�N� ------------------------------------------------------------------------
�D�      THE PROCEDURE THAT DRAWS THE FACETS THAT MAKE UP THE CUBE
�N� ------------------------------------------------------------------------
�
�
�� �edure_Draw_The_Cube
�
� � facet = 1 � 12
�
�9     point_1      = array_for_the_facets( facet , 1 )
�9     point_2      = array_for_the_facets( facet , 2 )
�9     point_3      = array_for_the_facets( facet , 3 )
�9     facet_colour = array_for_the_facets( facet , 4 )

D     first_x_position   = array_for_the_2D_points( point_1 , 1 )
D     first_y_position   = array_for_the_2D_points( point_1 , 2 )
"
,D     second_x_position  = array_for_the_2D_points( point_2 , 1 )
6D     second_y_position  = array_for_the_2D_points( point_2 , 2 )
@
JD     third_x_position   = array_for_the_2D_points( point_3 , 1 )
TD     third_y_position   = array_for_the_2D_points( point_3 , 2 )
^
hF     � *** The following lines implement the algorithm for     ***
rF     � *** determining whether or not the facet is currently   ***
|F     � *** visible. It's easy to read, and some users may      ***
�F     � *** evenh like to discover how it works in more detail. ***
�F     � *** Others are welcome to extract any part of this      ***
�F     � *** program for their own advantage!                    ***
�
�2     r0 = second_x_position - first_x_position
�A     r1 = third_y_position  - first_y_position : r2 = r0 * r1
�
�2     r0 = third_x_position  - first_x_position
�A     r1 = second_y_position - first_y_position : r3 = r0 * r1
�
�     � r2 - r3 > 0 �
�      � 0 , facet_colour
�5      �      first_x_position  , first_y_position
6      �      second_x_position , second_y_position
5      � 85 , third_x_position  , third_y_position

     �
&
0 � facet
:
D�
N
X
bN� ------------------------------------------------------------------------
lH�  PROCEDURE TO SWAP OUR SCREENS, KEEPING THE ANIMATION FLICKER FREE
vN� ------------------------------------------------------------------------
�
�
�"� �edure_Swap_The_Screen_Banks
�
� Ȗ
� BANK = BANK � 3
� ș 6,112,BANK
� ș 6,113,BANK � 3
� �
�
��
�
�
N� ------------------------------------------------------------------------
H�  THE PROCEDURE THAT READS THE 8 POINTS INTO THE ARRAY WE'VE SET UP
N� ------------------------------------------------------------------------
 
*
4)� �edure_Read_Points_Into_Their_Array
>
H � �d|H
R
\ � point = 1 � 8
f
p/     � X_POSITION , Y_POSITION , Z_POSITION
z
�:     array_for_the_3D_points( point , 1 ) = X_POSITION
�:     array_for_the_3D_points( point , 2 ) = Y_POSITION
�:     array_for_the_3D_points( point , 3 ) = Z_POSITION
�
� � point
�
��
�
�
�3� *** The data for the 8 points of the cube ***
�
�
�@� -10,+10 , +10 : REM The 4 points for the front of the cube
	� +10,+10 , +10
	� +10,-10 , +10
	� -10,-10 , +10
	$
	.@� -10,+10 , -10 : REM The 4 points for the back  of the cube
	8� +10,+10 , -10
	B� +10,-10 , -10
	L� -10,-10 , -10
	V
	`
	jN� ------------------------------------------------------------------------
	tI�  THE PROCEDURE THAT READS THE 12 FACETS INTO THE ARRAY WE'VE SET UP
	~N� ------------------------------------------------------------------------
	�
	�
	�)� �edure_Read_Facets_Into_Their_Array
	�
	� � �DnJ
	�
	� � facet = 1 � 12
	�
	�2     � JOIN_1 , JOIN_2 , JOIN_3 , FACET_COLOUR
	�
	�3     array_for_the_facets( facet , 1 ) = JOIN_1
	�3     array_for_the_facets( facet , 2 ) = JOIN_2
3     array_for_the_facets( facet , 3 ) = JOIN_3

9     array_for_the_facets( facet , 4 ) = FACET_COLOUR

 � facet
(
2�
<
F
P<� *** The data for the 12 facets to make up the cube ***
Z
d
n>� 1 , 2 , 3 ,  1 : REM The links to join up the front face
x� 1 , 3 , 4 ,  1
�
�=� 6 , 5 , 7 ,  3 : REM The links to join up the back face
�� 5 , 8 , 7 ,  3
�
�<� 2 , 6 , 7 ,  5 : REM The links to join up the RHS face
�� 2 , 7 , 3 ,  5
�
�<� 5 , 1 , 4 ,  7 : REM The links to join up the LHS face
�� 5 , 4 , 8 ,  7
�
�<� 5 , 6 , 2 ,  9 : REM The links to join up the top face
�� 5 , 2 , 1 ,  9
�
?� 4 , 3 , 8 , 11 : REM The links to join up the bottom face
� 3 , 7 , 8 , 11
�

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00000010  00 14 18 f4 20 50 72 6f  67 72 61 6d 20 3a 20 48  |.... Program : H|
00000020  41 52 2d 43 75 62 65 0d  00 1e 2d f4 20 20 20 20  |AR-Cube...-.    |
00000030  20 20 20 20 20 20 20 41  20 73 69 6d 70 6c 65 20  |       A simple |
00000040  33 44 20 63 75 62 65 20  69 6e 20 42 42 43 20 42  |3D cube in BBC B|
00000050  41 53 49 43 0d 00 28 1f  f4 20 41 75 74 68 6f 72  |ASIC..(.. Author|
00000060  20 20 3a 20 4b 65 76 69  6e 20 4a 20 53 77 69 6e  |  : Kevin J Swin|
00000070  74 6f 6e 0d 00 32 20 f4  20 56 65 72 73 69 6f 6e  |ton..2 . Version|
00000080  20 3a 20 41 63 6f 72 6e  20 41 35 30 30 30 2e 31  | : Acorn A5000.1|
00000090  2e 30 30 0d 00 3c 25 f4  20 44 61 74 65 20 20 20  |.00..<%. Date   |
000000a0  20 3a 20 54 68 75 72 73  64 61 79 20 35 74 68 20  | : Thursday 5th |
000000b0  4d 61 79 20 31 39 39 34  0d 00 46 04 0d 00 50 04  |May 1994..F...P.|
000000c0  0d 00 5a 23 ee 20 85 20  eb 20 eb 20 3a 20 f6 20  |..Z#. . . . : . |
000000d0  3a 20 f1 20 22 20 61 74  20 4c 69 6e 65 20 22 3b  |: . " at Line ";|
000000e0  9e 3a e0 0d 00 64 04 0d  00 6e 04 0d 00 78 4e f4  |.:...d...n...xN.|
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00000100  2d 2d 2d 2d 2d 2d 2d 2d  2d 2d 2d 2d 2d 2d 2d 2d  |----------------|
*
00000130  2d 2d 2d 2d 2d 2d 2d 2d  2d 0d 00 82 2f f4 20 20  |---------.../.  |
00000140  20 20 20 20 20 20 20 20  20 20 20 20 20 20 20 20  |                |
00000150  20 20 20 20 20 20 20 20  20 20 20 20 4d 41 49 4e  |            MAIN|
00000160  20 50 52 4f 47 52 41 4d  0d 00 8c 4e f4 20 2d 2d  | PROGRAM...N. --|
00000170  2d 2d 2d 2d 2d 2d 2d 2d  2d 2d 2d 2d 2d 2d 2d 2d  |----------------|
*
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000001c0  aa 10 eb 20 31 32 2b 31  32 38 20 3a 20 87 0d 00  |... 12+128 : ...|
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00000210  2d 2d 2d 2d 2d 2d 2d 2d  2d 2d 2d 2d 2d 2d 2d 2d  |----------------|
*
00000250  2d 2d 2d 2d 2d 2d 2d 0d  01 04 40 f4 20 20 20 20  |-------...@.    |
00000260  20 20 20 20 20 50 52 4f  43 45 44 55 52 45 20 54  |     PROCEDURE T|
00000270  4f 20 49 4e 49 54 49 41  4c 49 53 45 20 45 56 45  |O INITIALISE EVE|
00000280  52 59 54 48 49 4e 47 20  57 45 20 4e 45 45 44 20  |RYTHING WE NEED |
00000290  54 4f 20 4b 4e 4f 57 0d  01 0e 4e f4 20 2d 2d 2d  |TO KNOW...N. ---|
000002a0  2d 2d 2d 2d 2d 2d 2d 2d  2d 2d 2d 2d 2d 2d 2d 2d  |----------------|
*
000002e0  2d 2d 2d 2d 2d 0d 01 18  04 0d 01 22 04 0d 01 2c  |-----......"...,|
000002f0  17 dd 20 f2 65 64 75 72  65 5f 49 6e 69 74 69 61  |.. .edure_Initia|
00000300  6c 69 73 65 0d 01 36 04  0d 01 40 3b 20 f4 20 2a  |lise..6...@; . *|
00000310  2a 2a 20 50 6c 61 63 65  20 6f 75 72 20 6f 72 69  |** Place our ori|
00000320  67 69 6e 20 69 6e 20 74  68 65 20 6d 69 64 64 6c  |gin in the middl|
00000330  65 20 6f 66 20 74 68 65  20 73 63 72 65 65 6e 20  |e of the screen |
00000340  2a 2a 2a 0d 01 4a 11 20  c8 91 20 36 34 30 20 2c  |***..J. .. 640 ,|
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00000360  2a 2a 20 44 69 6d 65 6e  73 69 6f 6e 20 61 6c 6c  |** Dimension all|
00000370  20 74 68 65 20 61 72 72  61 79 73 20 74 68 61 74  | the arrays that|
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00000410  6e 74 73 2c 20 65 61 63  68 20 62 65 69 6e 67 20  |nts, each being |
00000420  61 6e 20 58 2c 59 20 20  20 28 32 44 29 0d 01 7c  |an X,Y   (2D)..||
00000430  62 20 de 20 61 72 72 61  79 5f 66 6f 72 5f 74 68  |b . array_for_th|
00000440  65 5f 66 61 63 65 74 73  28 20 31 32 20 2c 20 34  |e_facets( 12 , 4|
00000450  20 29 20 20 20 20 3a 20  f4 20 31 32 20 66 61 63  | )    : . 12 fac|
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00000490  01 86 04 0d 01 90 49 20  f4 20 2a 2a 2a 20 52 65  |......I . *** Re|
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000004b0  6d 61 74 69 6f 6e 20 77  65 20 6e 65 65 64 20 69  |mation we need i|
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000004d0  46 69 72 73 74 6c 79 2c  20 2a 2a 2a 0d 01 9a 49  |Firstly, ***...I|
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00000520  20 20 2a 2a 2a 0d 01 a4  49 20 f4 20 2a 2a 2a 20  |  ***...I . *** |
00000530  72 65 61 64 20 69 6e 20  61 6c 6c 20 74 68 65 20  |read in all the |
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00000570  ae 28 20 f2 65 64 75 72  65 5f 52 65 61 64 5f 50  |.( .edure_Read_P|
00000580  6f 69 6e 74 73 5f 49 6e  74 6f 5f 54 68 65 69 72  |oints_Into_Their|
00000590  5f 41 72 72 61 79 0d 01  b8 28 20 f2 65 64 75 72  |_Array...( .edur|
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000005b0  74 6f 5f 54 68 65 69 72  5f 41 72 72 61 79 0d 01  |to_Their_Array..|
000005c0  c2 04 0d 01 cc 0d 20 42  41 4e 4b 20 3d 20 31 0d  |...... BANK = 1.|
000005d0  01 d6 25 20 f2 65 64 75  72 65 5f 53 77 61 70 5f  |..% .edure_Swap_|
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000005f0  20 3a 20 db 0d 01 e0 25  20 f2 65 64 75 72 65 5f  | : ....% .edure_|
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00000610  42 61 6e 6b 73 20 3a 20  db 0d 01 ea 04 0d 01 f4  |Banks : ........|
00000620  3d 20 f4 20 2a 2a 2a 20  49 6e 69 74 69 61 6c 69  |= . *** Initiali|
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00000640  6f 66 20 74 68 65 20 6f  62 6a 65 63 74 20 69 6e  |of the object in|
00000650  20 73 70 61 63 65 20 2a  2a 2a 0d 01 fe 13 20 58  | space ***.... X|
00000660  5f 52 4f 54 41 54 49 4f  4e 20 3d 20 30 0d 02 08  |_ROTATION = 0...|
00000670  13 20 59 5f 52 4f 54 41  54 49 4f 4e 20 3d 20 30  |. Y_ROTATION = 0|
00000680  0d 02 12 13 20 5a 5f 52  4f 54 41 54 49 4f 4e 20  |.... Z_ROTATION |
00000690  3d 20 30 0d 02 1c 04 0d  02 26 3d 20 f4 20 2a 2a  |= 0......&= . **|
000006a0  2a 20 49 6e 69 74 69 61  6c 69 73 65 20 74 68 65  |* Initialise the|
000006b0  20 70 6f 73 69 74 69 6f  6e 20 6f 66 20 74 68 65  | position of the|
000006c0  20 6f 62 6a 65 63 74 20  69 6e 20 73 70 61 63 65  | object in space|
000006d0  20 2a 2a 2a 0d 02 30 3d  20 f4 20 2a 2a 2a 20 73  | ***..0= . *** s|
000006e0  6f 20 74 68 61 74 20 69  74 20 69 73 20 71 75 69  |o that it is qui|
000006f0  74 65 20 66 61 72 20 61  77 61 79 20 66 72 6f 6d  |te far away from|
00000700  20 75 73 20 20 20 20 20  20 20 20 20 20 20 2a 2a  | us           **|
00000710  2a 0d 02 3a 15 20 58 5f  50 4f 53 49 54 49 4f 4e  |*..:. X_POSITION|
00000720  20 3d 20 2b 20 30 0d 02  44 15 20 59 5f 50 4f 53  | = + 0..D. Y_POS|
00000730  49 54 49 4f 4e 20 3d 20  2b 20 30 0d 02 4e 15 20  |ITION = + 0..N. |
00000740  5a 5f 50 4f 53 49 54 49  4f 4e 20 3d 20 2b 35 30  |Z_POSITION = +50|
00000750  0d 02 58 04 0d 02 62 15  20 e3 20 73 63 61 6c 65  |..X...b. . scale|
00000760  20 3d 20 31 20 b8 20 31  35 0d 02 6c 14 20 20 72  | = 1 . 15..l.  r|
00000770  20 3d 20 73 63 61 6c 65  20 2a 20 31 36 0d 02 76  | = scale * 16..v|
00000780  0c 20 20 67 20 3d 20 39  36 0d 02 80 19 20 20 62  |.  g = 96....  b|
00000790  20 3d 20 31 32 38 20 2b  20 73 63 61 6c 65 20 2a  | = 128 + scale *|
000007a0  20 34 0d 02 8a 19 20 20  fb 20 73 63 61 6c 65 20  | 4....  . scale |
000007b0  2c 20 72 20 2c 20 67 20  2c 20 62 0d 02 94 0c 20  |, r , g , b.... |
000007c0  ed 20 73 63 61 6c 65 0d  02 9e 04 0d 02 a8 05 e1  |. scale.........|
000007d0  0d 02 b2 04 0d 02 bc 04  0d 02 c6 4e f4 20 2d 2d  |...........N. --|
000007e0  2d 2d 2d 2d 2d 2d 2d 2d  2d 2d 2d 2d 2d 2d 2d 2d  |----------------|
*
00000820  2d 2d 2d 2d 2d 2d 0d 02  d0 44 f4 20 20 20 20 20  |------...D.     |
00000830  20 4d 41 49 4e 20 50 52  4f 43 45 44 55 52 45 20  | MAIN PROCEDURE |
00000840  54 4f 20 43 4f 4e 54 52  4f 4c 20 54 48 45 20 53  |TO CONTROL THE S|
00000850  50 49 4e 4e 49 4e 47 20  43 55 42 45 20 4f 4e 20  |PINNING CUBE ON |
00000860  54 48 45 20 53 43 52 45  45 4e 0d 02 da 4e f4 20  |THE SCREEN...N. |
00000870  2d 2d 2d 2d 2d 2d 2d 2d  2d 2d 2d 2d 2d 2d 2d 2d  |----------------|
*
000008b0  2d 2d 2d 2d 2d 2d 2d 2d  0d 02 e4 04 0d 02 ee 04  |--------........|
000008c0  0d 02 f8 11 dd 20 f2 65  64 75 72 65 5f 43 75 62  |..... .edure_Cub|
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*
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*
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*
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*
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