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
 Variations: See code variations for this subroutine in the different versions
 References: This subroutine is called as follows:
             * ADDBYT calls LOIN
             * TTX66 calls LOIN


 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


                        \ In the 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
                        \
                        \ In the 6502 Second Processor version, there are three
                        \ different routines. In the parasite, LL30 draws a
                        \ one-segment line, while LOIN draws multi-segment
                        \ lines. Both of these ask the I/O processor to do the
                        \ actual drawing, and it uses a routine called... wait
                        \ for it... LOIN
                        \
                        \ This, then, is the I/O processor's LOIN routine, which
                        \ is not the same as LL30, or the other LOIN. Got that?

.LOIN

 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

 BEQ HLOIN2             \ If A = 0 then Y1 = Y2, which means the line is
                        \ horizontal, so jump to HLOIN2 to draw a horizontal
                        \ line instead of applying Bresenham's line algorithm

 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