.ProjectParticleOntoScreen CMN R2, #&80000000 \ If R2 + &80000000 produces a carry, then MOVCS PC, R14 \ the particle is too far away to be \ visible, so return from the subroutine \ with the C flag set MOVS R3, R0 \ Set R3 = |R0| RSBMI R3, R3, #0 \ = |x| MVNMI R5, R3 \ If R0 is negative, set R5 = ~R3 MOVPL R5, R3 \ If R0 is positive, set R5 = R3 MOVS R4, R1 \ Set R4 = |R1| RSBMI R4, R4, #0 \ = |y| MVNMI R6, R4 \ If R1 is negative, set R6 = ~R4 MOVPL R6, R4 \ If R1 is positive, set R6 = R4 ORR R5, R5, R6 \ Set R5 = R5 OR R6 OR R2 ORR R5, R5, R2 \ = |R0| OR |R1| OR R2 ORR R5, R5, #1 \ = |x| OR |y| OR z \ \ And round it up so it is non-zero \ \ So this sets R5 to a number that is \ greater than |x|, |y| and z, so R5 is \ therefore an upper bound on the values of \ all three coordinates \ We now work out how many times we can \ scale up R5 so that it is as large as \ possible but still fits within a 32-bit \ word MOV R6, #0 \ Set R6 = 0 to use as the scale factor in \ the following loop .ppar1 MOVS R5, R5, LSL #1 \ Shift R5 to the left until the top bit is ADDPL R6, R6, #1 \ set, incrementing R6 for each shift so R6 BPL ppar1 \ contains the scale factor we have applied \ to R5 \ \ So this scales R5 as high as possible \ while still staying within 32 bits, with \ the scale factor given in R6 MOV R2, R2, LSL R6 \ We now scale up the updated coordinate MOV R3, R3, LSL R6 \ (|x|, |y|, z) in (R3, R4, R2) by the scale MOV R4, R4, LSL R6 \ factor in R6, as we know the result will \ stay within 32-bit words CMP R3, R2 \ If R3 >= R2 or R4 >= R2, then at least one CMPCC R4, R2 \ of these is true: MOVCS PC, R14 \ \ |x| >= z or |y| >= z \ \ so return from the subroutine with C flag \ set to indicate the particle is off-screen \ \ This is the case when the particle has a \ greater viewing angle then 45 degrees in \ either direction, in which case we don't \ draw the particle on-screen STMFD R13!, {R7, R14} \ Store the registers that we want to use on \ the stack so they can be preserved MOV R7, R2 \ Set R7 = R2 \ = z \ \ where the value of z is scaled up \ We now calculate R6 = R4 / R7 using the \ shift-and-subtract algorithm MOV R6, #0 \ Set R6 = 0 to use for building the sum in \ our shift-and-subtract division result MOV R14, #&200 \ Set bit 9 in R14 to act as our shifted \ division bit, so we populate ten bits of \ the result .ppar2 MOVS R4, R4, LSL #1 \ Shift R4 left by one place CMPCC R4, R7 \ If we just shifted a zero out of R4, set \ the C flag if R4 >= R7 SUBCS R4, R4, R7 \ The numerator in R4 is bigger than the ORRCS R6, R6, R14 \ denominator in R7, so subtract the \ denominator from the numerator and set the \ corresponding bit in the result MOVS R14, R14, LSR #1 \ Shift R14 right by one place, shifting bit \ 0 into the C flag BCC ppar2 \ Loop back until we shift a 1 out of R14 MOVS R6, R6, LSL #22 \ Shift the result in R6 left as far as \ possible so it still fits in to 32 bits \ (as the result contains ten bits), so now \ we have: \ \ R6 = R4 / R7 \ = |y| / z \ \ where |y| and z are both scaled up by the \ same factor MOV R5, #0 \ Set R5 = R3 / R2 using the same algorithm MOV R14, #&200 \ as above \ \ This is the first part of the algorithm .ppar3 MOVS R3, R3, LSL #1 \ This is the second part of the algorithm, CMPCC R3, R2 \ so we now have: SUBCS R3, R3, R2 \ ORRCS R5, R5, R14 \ R5 = R3 / R2 MOVS R14, R14, LSR #1 \ = |x| / z BCC ppar3 \ MOVS R5, R5, LSL #22 \ where |x| and z are both scaled up by the \ same factor MOV R5, R5, LSR #24 \ Shift both division results down so we MOV R6, R6, LSR #24 \ only keep the top byte of each result TEQ R0, #0 \ If the original R0 argument was positive, ADDPL R0, R5, #160 \ set: RSBMI R0, R5, #160 \ \ R0 = 160 + R5 \ = 160 + |x| / z \ = 160 + x / z \ \ otherwise set: \ \ R0 = 160 - R5 \ = 160 - |x| / z \ = 160 + x / z \ \ So this sets R0 as follows, where x and z \ are the original particle's coordinates: \ \ R0 = 160 + x / z TEQ R1, #0 \ If the original R1 argument was positive, ADDPL R1, R6, #64 \ set: RSBMI R1, R6, #64 \ \ R1 = 64 + R6 \ = 64 + |y| / z \ = 64 + y / z \ \ otherwise set: \ \ R1 = 64 - R6 \ = 64 - |y| / z \ = 64 + y / z \ \ So this sets R1 as follows, where y and z \ are the original particle's coordinates: \ \ R1 = 64 + y / z CMP R0, #320 \ Set the C flag if either of these is true: CMPCC R1, #239 \ \ screen x-coordinate in R0 >= 320 \ \ screen y-coordinate in R1 >= 239 \ \ to indicate that the particle is \ off-screen LDMFD R13!, {R7, PC} \ Retrieve the registers that we stored on \ the stack and return from the subroutineName: ProjectParticleOntoScreen [Show more] Type: Subroutine Category: Maths (Geometry) Summary: Project a 3D particle coordinate onto the screen Deep dive: Particles and particle clouds Projecting onto the screenContext: See this subroutine in context in the source code References: This subroutine is called as follows: * MoveAndDrawParticles (Part 4 of 4) calls ProjectParticleOntoScreen
This routine projects a 3D coordinate (x, y, z) into screen coordinates, as follows: screen x-coordinate = 160 + x / z screen y-coordinate = 64 + y / z The screen coordinate is deemed on-screen when it is within the following valid ranges: screen x is in the range 0 to 319 screen y is in the range 0 to 238 and is at less than a 45-degree viewing angle (i.e. within a viewing cone of 45 degrees). The particle is deemed visible if its z-coordinate is less than &80000000, and is not projected if it is further away than this. The y-coordinate is the screen height (256 pixels) minus the two text lines that are reserved for the score bar at the top of the screen (16 pixels).
Arguments: (R0, R1, R2) Particle coordinates in (x, y, z)
Returns: (R0, R1) Projected screen coordinates (x, y) C flag C flag is set if the particle is off-screen, clear if it is on-screen
[X]
Label ppar1 is local to this routine
[X]
Label ppar2 is local to this routine
[X]
Label ppar3 is local to this routine