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:
             * LOIN calls via LOINQ
             * TTX66 calls via LOINQ


 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


 Other entry points:

   LOINQ                Draw a one-segment line from (X1, Y1) to (X2, Y2)


.HLOIN22

 JMP HLOIN3             \ This instruction doesn't appear to be used anywhere

                        \ 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 BBC Master version, there are two different
                        \ routines: LOINQ draws a one-segment line, while LOIN
                        \ draws individual segments of multi-segment lines (the
                        \ distinction being that we switch to screen memory at
                        \ the start of LOINQ and back out again after drawing
                        \ the line, while LOIN just draws the line)

.LOINQ

 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 HLOIN22            \ This instruction is commented out in the original
                        \ source

 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