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⌂ ∞ ▽ Elite on the 6502

Drawing lines: LOINQ (Part 5 of 7)

[BBC Master version]

       Name: LOINQ (Part 5 of 7)                                     [Show more]
       Type: Subroutine
   Category: Drawing lines
    Summary: Draw a line: Line has a steep gradient, step up along y-axis
  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: No direct references to this subroutine in this source file




 This routine draws a line from (X1, Y1) to (X2, Y2). It has multiple stages.
 If we get here, then:

   * |delta_y| >= |delta_x|

   * The line is closer to being vertical than horizontal

   * We are going to step up along the y-axis

   * We potentially swap coordinates to make sure Y1 >= Y2



.STPY

 LDY Y1                 \ Set A = Y = Y1
 TYA

 LDX X1                 \ Set X = X1

 CPY Y2                 \ If Y1 >= Y2, jump down to LI15, as the coordinates are
 BCS LI15               \ already in the order that we want

 DEC SWAP               \ Otherwise decrement SWAP from 0 to &FF, to denote that
                        \ we are swapping the coordinates around

 LDA X2                 \ Swap the values of X1 and X2
 STA X1
 STX X2

 TAX                    \ Set X = X1

 LDA Y2                 \ Swap the values of Y1 and Y2
 STA Y1
 STY Y2

 TAY                    \ Set Y = A = Y1

.LI15

                        \ By this point we know the line is vertical-ish and
                        \ Y1 >= Y2, so we're going from top to bottom as we go
                        \ from Y1 to Y2

 LDA ylookup,Y          \ Look up the page number of the character row that
 STA SC+1               \ contains the pixel with the y-coordinate in Y1, and
                        \ store it in the high byte of SC(1 0) at SC+1, so the
                        \ high byte of SC is set correctly for drawing our line

 TXA                    \ Set A = 2 * bits 2-6 of X1
 AND #%11111100         \
 ASL A                  \ and shift bit 7 of X1 into the C flag

 STA SC                 \ Store this value in SC, so SC(1 0) now contains the
                        \ screen address of the far left end (x-coordinate = 0)
                        \ of the horizontal pixel row that we want to draw the
                        \ start of our line on

 BCC P%+4               \ If bit 7 of X1 was set, so X1 > 127, increment the
 INC SC+1               \ high byte of SC(1 0) to point to the second page on
                        \ this screen row, as this page contains the right half
                        \ of the row

 TXA                    \ Set X = X1 mod 4, which is the horizontal pixel number
 AND #3                 \ within the character block where the line starts (as
 TAX                    \ each pixel line in the character block is 4 pixels
                        \ wide)

 LDA TWOS,X             \ Fetch a 1-pixel byte from TWOS where pixel X is set,
 STA R                  \ and store it in R

                        \ The following section calculates:
                        \
                        \   P = P / Q
                        \     = |delta_x| / |delta_y|
                        \
                        \ using the log tables at logL and log to calculate:
                        \
                        \   A = log(P) - log(Q)
                        \     = log(|delta_x|) - log(|delta_y|)
                        \
                        \ by first subtracting the low bytes of the logarithms
                        \ from the table at LogL, and then subtracting the high
                        \ bytes from the table at log, before applying the
                        \ antilog to get the result of the division and putting
                        \ it in P

 LDX P                  \ Set X = |delta_x|

 BEQ LIfudge            \ If |delta_x| = 0, jump to LIfudge to return 0 as the
                        \ result of the division

 LDA logL,X             \ Set A = log(P) - log(Q)
 LDX Q                  \       = log(|delta_x|) - log(|delta_y|)
 SEC                    \
 SBC logL,X             \ by first subtracting the low bytes of log(P) - log(Q)

 LDX P                  \ And then subtracting the high bytes of log(P) - log(Q)
 LDA log,X              \ so now A contains the high byte of log(P) - log(Q)
 LDX Q
 SBC log,X

 BCS LIlog3             \ If the subtraction fitted into one byte and didn't
                        \ underflow, then log(P) - log(Q) < 256, so we jump to
                        \ LIlog3 to return a result of 255

 TAX                    \ Otherwise we set A to the A-th entry from the antilog
 LDA alogh,X            \ table so the result of the division is now in A

 JMP LIlog2             \ Jump to LIlog2 to return the result

.LIlog3

 LDA #255               \ The division is very close to 1, so set A to the
                        \ closest possible answer to 256, i.e. 255

.LIlog2

 STA P                  \ Store the result of the division in P, so we have:
                        \
                        \   P = |delta_x| / |delta_y|

.LIfudge

 LDX Q                  \ Set X = Q
                        \       = |delta_y|

 BEQ LIEX7              \ If |delta_y| = 0, jump down to LIEX7 to return from
                        \ the subroutine

 INX                    \ Set X = Q + 1
                        \       = |delta_y| + 1
                        \
                        \ We add 1 so we can skip the first pixel plot if the
                        \ line is being drawn with swapped coordinates

 LDA X2                 \ Set A = X2 - X1
 SEC
 SBC X1

 BCS P%+6               \ If X2 >= X1 then skip the following two instructions

 JMP LFT                \ If X2 < X1 then jump to LFT, as we need to draw the
                        \ line to the left and down

.LIEX7

 RTS                    \ Return from the subroutine