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Drawing lines: LOIN (Part 5 of 7)

[BBC Master version]

Name: LOIN (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