Skip to navigation

BBC Micro Elite

Drawing planets: PLL1

Name: PLL1 [View in context] Type: Subroutine Category: Drawing planets Summary: Draw Saturn on the loading screen
Part 1 (PLL1) x 1280 - planet * Draw pixels at (x, y) where: r1 = random number from 0 to 255 r2 = random number from 0 to 255 (r1^2 + r1^2) < 128^2 y = r2, squished into 64 to 191 by negation x = SQRT(128^2 - (r1^2 + r1^2)) / 2 Part 2 (PLL2) x 477 - stars * Draw pixels at (x, y) where: y = random number from 0 to 255 y = random number from 0 to 255 (x^2 + y^2) div 256 > 17 Part 3 (PLL3) x 1280 - rings * Draw pixels at (x, y) where: r5 = random number from 0 to 255 r6 = random number from 0 to 255 r7 = r5, squashed into -32 to 31 32 <= (r5^2 + r6^2 + r7^2) / 256 <= 79 Draw 50% fewer pixels when (r6^2 + r7^2) / 256 <= 16 x = r5 + r7 y = r5 Draws pixels within the diagonal band of horizontal width 64, from top-left to bottom-right of the screen.
.PLL1 { \ The following loop iterates CNT(1 0) times, i.e. &500 \ or 1280 times LDA VIA+4 \ Read the 6522 System VIA T1C-L timer 1 low-order STA RAND+1 \ counter, which increments 1000 times a second so this \ will be pretty random, and store it in RAND+1 among \ the hard-coded random seeds in RAND JSR DORND \ Set A and X to random numbers, say A = r1 JSR SQUA2 \ Set (A P) = A * A \ = r1^2 STA ZP+1 \ Set ZP(1 0) = (A P) LDA P \ = r1^2 STA ZP JSR DORND \ Set A and X to random numbers, say A = r2 STA YY \ Set YY = A \ = r2 JSR SQUA2 \ Set (A P) = A * A \ = r2^2 TAX \ Set (X P) = (A P) \ = r2^2 LDA P \ Set (A ZP) = (X P) + ZP(1 0) ADC ZP \ STA ZP \ first adding the low bytes TXA \ And then adding the high bytes ADC ZP+1 BCS PLC1 \ If the addition overflowed, jump down to PLC1 to skip \ to the next pixel STA ZP+1 \ Set ZP(1 0) = (A ZP) \ = r1^2 + r2^2 LDA #1 \ Set ZP(1 0) = &4001 - ZP(1 0) - (1 - C) SBC ZP \ = 128^2 - ZP(1 0) STA ZP \ \ (as the C flag is clear), first subtracting the low \ bytes LDA #&40 \ And then subtracting the high bytes SBC ZP+1 STA ZP+1 BCC PLC1 \ If the subtraction underflowed, jump down to PLC1 to \ skip to the next pixel \ If we get here, then both calculations fitted into \ 16 bits, and we have: \ \ ZP(1 0) = 128^2 - (r1^2 + r2^2) \ \ where ZP(1 0) >= 0 JSR ROOT \ Set ZP = SQRT(ZP(1 0)) LDA ZP \ Set X = ZP >> 1 LSR A \ = SQRT(128^2 - (a^2 + b^2)) / 2 TAX LDA YY \ Set A = YY \ = r2 CMP #128 \ If YY >= 128, set the C flag (so the C flag is now set \ to bit 7 of A) ROR A \ Rotate A and set the sign bit to the C flag, so bits \ 6 and 7 are now the same, i.e. A is a random number in \ one of these ranges: \ \ %00000000 - %00111111 = 0 to 63 (r2 = 0 - 127) \ %11000000 - %11111111 = 192 to 255 (r2 = 128 - 255) \ \ The PIX routine flips bit 7 of A before drawing, and \ that makes -A in these ranges: \ \ %10000000 - %10111111 = 128-191 \ %01000000 - %01111111 = 64-127 \ \ so that's in the range 64 to 191 JSR PIX \ Draw a pixel at screen coordinate (X, -A), i.e. at \ \ (ZP / 2, -A) \ \ where ZP = SQRT(128^2 - (r1^2 + r2^2)) \ \ So this is the same as plotting at (x, y) where: \ \ r1 = random number from 0 to 255 \ r1 = random number from 0 to 255 \ (r1^2 + r1^2) < 128^2 \ \ y = r2, squished into 64 to 191 by negation \ \ x = SQRT(128^2 - (r1^2 + r1^2)) / 2 \ \ which is what we want .PLC1 DEC CNT \ Decrement the counter in CNT (the low byte) BNE PLL1 \ Loop back to PLL1 until CNT = 0 DEC CNT+1 \ Decrement the counter in CNT+1 (the high byte) BNE PLL1 \ Loop back to PLL1 until CNT+1 = 0 LDX #&C2 \ Set the low byte of EXCN(1 0) to &C2, so we now have STX EXCN \ EXCN(1 0) = &03C2, which we will use in the IRQ1 \ handler (this has nothing to do with drawing Saturn, \ it's all part of the copy protection) .PLL2 JSR DORND \ Set A and X to random numbers, say A = r3 TAX \ Set X = A \ = r3 JSR SQUA2 \ Set (A P) = A * A \ = r3^2 STA ZP+1 \ Set ZP+1 = A \ = r3^2 / 256 JSR DORND \ Set A and X to random numbers, say A = r4 STA YY \ Set YY = r4 JSR SQUA2 \ Set (A P) = A * A \ = r4^2 ADC ZP+1 \ Set A = A + r3^2 / 256 \ = r4^2 / 256 + r3^2 / 256 \ = (r3^2 + r4^2) / 256 CMP #&11 \ If A < 17, jump down to PLC2 to skip to the next pixel BCC PLC2 LDA YY \ Set A = r4 JSR PIX \ Draw a pixel at screen coordinate (X, -A), i.e. at \ (r3, -r4), where (r3^2 + r4^2) / 256 >= 17 \ \ Negating a random number from 0 to 255 gives the same \ thing, so this is the same as plotting at (x, y) \ where: \ \ x = random number from 0 to 255 \ y = random number from 0 to 255 \ (x^2 + y^2) div 256 >= 17 \ \ which is what we want .PLC2 DEC CNT2 \ Decrement the counter in CNT2 (the low byte) BNE PLL2 \ Loop back to PLL2 until CNT2 = 0 DEC CNT2+1 \ Decrement the counter in CNT2+1 (the high byte) BNE PLL2 \ Loop back to PLL2 until CNT2+1 = 0 LDX MHCA \ Set the low byte of BLPTR(1 0) to the contents of MHCA STX BLPTR \ (which is &CA), so we now have BLPTR(1 0) = &03CA, \ which we will use in the IRQ1 handler (this has \ nothing to do with drawing Saturn, it's all part of \ the copy protection) LDX #&C6 \ Set the low byte of BLN(1 0) to &C6, so we now have STX BLN \ BLN(1 0) = &03C6, which we will use in the IRQ1 \ handler (this has nothing to do with drawing Saturn, \ it's all part of the copy protection) .PLL3 JSR DORND \ Set A and X to random numbers, say A = r5 STA ZP \ Set ZP = r5 JSR SQUA2 \ Set (A P) = A * A \ = r5^2 STA ZP+1 \ Set ZP+1 = A \ = r5^2 / 256 JSR DORND \ Set A and X to random numbers, say A = r6 STA YY \ Set YY = r6 JSR SQUA2 \ Set (A P) = A * A \ = r6^2 STA T \ Set T = A \ = r6^2 / 256 ADC ZP+1 \ Set ZP+1 = A + r5^2 / 256 STA ZP+1 \ = r6^2 / 256 + r5^2 / 256 \ = (r5^2 + r6^2) / 256 LDA ZP \ Set A = ZP \ = r5 CMP #128 \ If A >= 128, set the C flag (so the C flag is now set \ to bit 7 of ZP, i.e. bit 7 of A) ROR A \ Rotate A and set the sign bit to the C flag, so bits \ 6 and 7 are now the same CMP #128 \ If A >= 128, set the C flag (so again, the C flag is \ set to bit 7 of A) ROR A \ Rotate A and set the sign bit to the C flag, so bits \ 5-7 are now the same, i.e. A is a random number in one \ of these ranges: \ \ %00000000 - %00011111 = 0-31 \ %11100000 - %11111111 = 224-255 \ \ In terms of signed 8-bit integers, this is from -32 to \ 31. Let's call it r7 ADC YY \ Set X = A + YY TAX \ = r7 + r6 JSR SQUA2 \ Set (A P) = r7 * r7 TAY \ Set Y = A \ = r7 * r7 / 256 ADC ZP+1 \ Set A = A + ZP+1 \ = r7^2 / 256 + (r5^2 + r6^2) / 256 \ = (r5^2 + r6^2 + r7^2) / 256 BCS PLC3 \ If the addition overflowed, jump down to PLC3 to skip \ to the next pixel CMP #80 \ If A >= 80, jump down to PLC3 to skip to the next BCS PLC3 \ pixel CMP #32 \ If A < 32, jump down to PLC3 to skip to the next BCC PLC3 \ pixel TYA \ Set A = Y + T ADC T \ = r7^2 / 256 + r6^2 / 256 \ = (r6^2 + r7^2) / 256 CMP #16 \ If A > 16, skip to PL1 to plot the pixel BCS PL1 LDA ZP \ If ZP is positive (50% chance), jump down to PLC3 to BPL PLC3 \ skip to the next pixel .PL1 LDA YY \ Set A = YY \ = r6 JSR PIX \ Draw a pixel at screen coordinate (X, -A), where: \ \ X = (random -32 to 31) + r6 \ A = r6 \ \ Negating a random number from 0 to 255 gives the same \ thing, so this is the same as plotting at (x, y) \ where: \ \ r5 = random number from 0 to 255 \ r6 = random number from 0 to 255 \ r7 = r5, squashed into -32 to 31 \ \ x = r5 + r7 \ y = r5 \ \ 32 <= (r5^2 + r6^2 + r7^2) / 256 <= 79 \ Draw 50% fewer pixels when (r6^2 + r7^2) / 256 <= 16 \ \ which is what we want .PLC3 DEC CNT3 \ Decrement the counter in CNT3 (the low byte) BNE PLL3 \ Loop back to PLL3 until CNT3 = 0 DEC CNT3+1 \ Decrement the counter in CNT3+1 (the high byte) BNE PLL3 \ Loop back to PLL3 until CNT3+1 = 0