Drawing lines: LOIN (Part 1 of 7)

       Name: LOIN (Part 1 of 7)                                      [Show more]
       Type: Subroutine
   Category: Drawing lines
    Summary: Draw a line: Calculate the line gradient in the form of deltas
  Deep dive: Bresenham's line algorithm
    Context: See this subroutine in context in the source code
 References: This subroutine is called as follows:
             * BLINE calls LOIN
             * TTX66 calls LOIN
             * LL9 (Part 12 of 12) calls via LL30
             * TT15 calls via LL30


 This routine draws a line from (X1, Y1) to (X2, Y2). It has multiple stages.
 This stage calculates the line deltas.


 Arguments:

   X1                   The screen x-coordinate of the start of the line

   Y1                   The screen y-coordinate of the start of the line

   X2                   The screen x-coordinate of the end of the line

   Y2                   The screen y-coordinate of the end of the line


 Returns:

   Y                    Y is preserved


 Other entry points:

   LL30                 LL30 is a synonym for LOIN and draws a line from
                        (X1, Y1) to (X2, Y2)


.LL30

 SKIP 0                 \ LL30 is a synonym for LOIN
                        \
                        \ In the BBC Micro cassette and disc versions of Elite,
                        \ LL30 and LOIN are synonyms for the same routine,
                        \ presumably because the two developers each had their
                        \ own line routines to start with, and then chose one of
                        \ them for the final game

.LOIN

 STY YSAV               \ Store Y into YSAV, so we can preserve it across the
                        \ call to this subroutine

 LDA #128               \ Set S = 128, which is the starting point for the
 STA S                  \ slope error (representing half a pixel)

 ASL A                  \ Set SWAP = 0, as %10000000 << 1 = 0
 STA SWAP

 LDA X2                 \ Set A = X2 - X1
 SBC X1                 \       = delta_x
                        \
                        \ This subtraction works as the ASL A above sets the C
                        \ flag

 BCS LI1                \ If X2 > X1 then A is already positive and we can skip
                        \ the next three instructions

 EOR #%11111111         \ Negate the result in A by flipping all the bits and
 ADC #1                 \ adding 1, i.e. using two's complement to make it
                        \ positive

 SEC                    \ Set the C flag, ready for the subtraction below

.LI1

 STA P                  \ Store A in P, so P = |X2 - X1|, or |delta_x|

 LDA Y2                 \ Set A = Y2 - Y1
 SBC Y1                 \       = delta_y
                        \
                        \ This subtraction works as we either set the C flag
                        \ above, or we skipped that SEC instruction with a BCS

 BCS LI2                \ If Y2 > Y1 then A is already positive and we can skip
                        \ the next two instructions

 EOR #%11111111         \ Negate the result in A by flipping all the bits and
 ADC #1                 \ adding 1, i.e. using two's complement to make it
                        \ positive

.LI2

 STA Q                  \ Store A in Q, so Q = |Y2 - Y1|, or |delta_y|

 CMP P                  \ If Q < P, jump to STPX to step along the x-axis, as
 BCC STPX               \ the line is closer to being horizontal than vertical

 JMP STPY               \ Otherwise Q >= P so jump to STPY to step along the
                        \ y-axis, as the line is closer to being vertical than
                        \ horizontal