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BBC Micro Elite

Drawing ships: LL9 (Part 6 of 11)

Name: LL9 (Part 6 of 11) [View in context] Type: Subroutine Category: Drawing ships Summary: Draw ship: Calculate the visibility of each of the ship's vertices Deep dive: Calculating vertex coordinates
This section calculates the visibility of each of the ship's vertices, and for those that are visible, it starts the process of calculating the screen coordinates of each vertex
.LL42 \ The first task is to set up the inverse matrix, ready \ for us to send to the dot product routine at LL51. \ Back up in part 3, we set up the following variables: \ \ * XX16(1 0) = sidev_x \ * XX16(3 2) = sidev_y \ * XX16(5 4) = sidev_z \ \ * XX16(7 6) = roofv_x \ * XX16(9 8) = roofv_y \ * XX16(11 10) = roofv_z \ \ * XX16(13 12) = nosev_x \ * XX16(15 14) = nosev_y \ * XX16(17 16) = nosev_z \ \ and we then scaled the vectors to give the following: \ \ * XX16 = scaled |sidev_x| \ * XX16+2 = scaled |sidev_y| \ * XX16+4 = scaled |sidev_z| \ \ * XX16+6 = scaled |roofv_x| \ * XX16+8 = scaled |roofv_y| \ * XX16+10 = scaled |roofv_z| \ \ * XX16+12 = scaled |nosev_x| \ * XX16+14 = scaled |nosev_y| \ * XX16+16 = scaled |nosev_z| \ \ We now need to rearrange these locations so they \ effectively transpose the matrix into its inverse LDY XX16+2 \ Set XX16+2 = XX16+6 = scaled |roofv_x| LDX XX16+3 \ Set XX16+3 = XX16+7 = roofv_x_hi LDA XX16+6 \ Set XX16+6 = XX16+2 = scaled |sidev_y| STA XX16+2 \ Set XX16+7 = XX16+3 = sidev_y_hi LDA XX16+7 STA XX16+3 STY XX16+6 STX XX16+7 LDY XX16+4 \ Set XX16+4 = XX16+12 = scaled |nosev_x| LDX XX16+5 \ Set XX16+5 = XX16+13 = nosev_x_hi LDA XX16+12 \ Set XX16+12 = XX16+4 = scaled |sidev_z| STA XX16+4 \ Set XX16+13 = XX16+5 = sidev_z_hi LDA XX16+13 STA XX16+5 STY XX16+12 STX XX16+13 LDY XX16+10 \ Set XX16+10 = XX16+14 = scaled |nosev_y| LDX XX16+11 \ Set XX16+11 = XX16+15 = nosev_y_hi LDA XX16+14 \ Set XX16+14 = XX16+10 = scaled |roofv_z| STA XX16+10 \ Set XX16+15 = XX16+11 = roofv_z LDA XX16+15 STA XX16+11 STY XX16+14 STX XX16+15 \ So now we have the following sign-magnitude variables \ containing parts of the scaled orientation vectors: \ \ XX16(1 0) = scaled sidev_x \ XX16(3 2) = scaled roofv_x \ XX16(5 4) = scaled nosev_x \ \ XX16(7 6) = scaled sidev_y \ XX16(9 8) = scaled roofv_y \ XX16(11 10) = scaled nosev_y \ \ XX16(13 12) = scaled sidev_z \ XX16(15 14) = scaled roofv_z \ XX16(17 16) = scaled nosev_z \ \ which is what we want, as the various vectors are now \ arranged so we can use LL51 to multiply by the \ transpose (i.e. the inverse of the matrix) LDY #8 \ Fetch byte #8 of the ship's blueprint, which is the LDA (XX0),Y \ number of vertices * 8, and store it in XX20 STA XX20 \ We now set V(1 0) = XX0(1 0) + 20, so V(1 0) points \ to byte #20 of the ship's blueprint, which is always \ where the vertex data starts (i.e. just after the 20 \ byte block that define the ship's characteristics) LDA XX0 \ We start with the low bytes CLC ADC #20 STA V LDA XX0+1 \ And then do the high bytes ADC #0 STA V+1 LDY #0 \ We are about to step through all the vertices, using \ Y as a counter. There are six data bytes for each \ vertex, so we will increment Y by 6 for each iteration \ so it can act as an offset from V(1 0) to the current \ vertex's data STY CNT \ Set CNT = 0, which we will use as a pointer to the \ heap at XX3, starting it at zero so the heap starts \ out empty .LL48 STY XX17 \ Set XX17 = Y, so XX17 now contains the offset of the \ current vertex's data LDA (V),Y \ Fetch byte #0 for this vertex into XX15, so: STA XX15 \ \ XX15 = magnitude of the vertex's x-coordinate INY \ Increment Y to point to byte #1 LDA (V),Y \ Fetch byte #1 for this vertex into XX15+2, so: STA XX15+2 \ \ XX15+2 = magnitude of the vertex's y-coordinate INY \ Increment Y to point to byte #2 LDA (V),Y \ Fetch byte #2 for this vertex into XX15+4, so: STA XX15+4 \ \ XX15+4 = magnitude of the vertex's z-coordinate INY \ Increment Y to point to byte #3 LDA (V),Y \ Fetch byte #3 for this vertex into T, so: STA T \ \ T = %xyz vvvvv, where: \ \ * Bits 0-4 = visibility distance, beyond which the \ vertex is not shown \ \ * Bits 7-5 = the sign bits of x, y and z AND #%00011111 \ Extract bits 0-4 to get the visibility distance CMP XX4 \ If XX4 > the visibility distance, where XX4 contains BCC LL49-3 \ the ship's z-distance reduced to 0-31 (which we set in \ part 2), then this vertex is too far away to be \ visible, so jump down to LL50 (via the JMP instruction \ in LL49-3) to move on to the next vertex INY \ Increment Y to point to byte #4 LDA (V),Y \ Fetch byte #4 for this vertex into P, so: STA P \ \ P = %ffff ffff, where: \ \ * Bits 0-3 = the number of face 1 \ \ * Bits 4-7 = the number of face 2 AND #%00001111 \ Extract the number of face 1 into X TAX LDA XX2,X \ If XX2+X is non-zero then we decided in part 5 that BNE LL49 \ face 1 is visible, so jump to LL49 LDA P \ Fetch byte #4 for this vertex into A LSR A \ Shift right four times to extract the number of face 2 LSR A \ from bits 4-7 into X LSR A LSR A TAX LDA XX2,X \ If XX2+X is non-zero then we decided in part 5 that BNE LL49 \ face 2 is visible, so jump to LL49 INY \ Increment Y to point to byte #5 LDA (V),Y \ Fetch byte #5 for this vertex into P, so: STA P \ \ P = %ffff ffff, where: \ \ * Bits 0-3 = the number of face 3 \ \ * Bits 4-7 = the number of face 4 AND #%00001111 \ Extract the number of face 1 into X TAX LDA XX2,X \ If XX2+X is non-zero then we decided in part 5 that BNE LL49 \ face 3 is visible, so jump to LL49 LDA P \ Fetch byte #5 for this vertex into A LSR A \ Shift right four times to extract the number of face 4 LSR A \ from bits 4-7 into X LSR A LSR A TAX LDA XX2,X \ If XX2+X is non-zero then we decided in part 5 that BNE LL49 \ face 4 is visible, so jump to LL49 JMP LL50 \ If we get here then none of the four faces associated \ with this vertex are visible, so this vertex is also \ not visible, so jump to LL50 to move on to the next \ vertex .LL49 LDA T \ Fetch byte #5 for this vertex into A and store it, so STA XX15+1 \ XX15+1 now has the sign of the vertex's x-coordinate ASL A \ Shift A left and store it, so XX15+3 now has the sign STA XX15+3 \ of the vertex's y-coordinate ASL A \ Shift A left and store it, so XX15+5 now has the sign STA XX15+5 \ of the vertex's z-coordinate \ By this point we have the following: \ \ XX15(1 0) = vertex x-coordinate \ XX15(3 2) = vertex y-coordinate \ XX15(5 4) = vertex z-coordinate \ \ XX16(1 0) = scaled sidev_x \ XX16(3 2) = scaled roofv_x \ XX16(5 4) = scaled nosev_x \ \ XX16(7 6) = scaled sidev_y \ XX16(9 8) = scaled roofv_y \ XX16(11 10) = scaled nosev_y \ \ XX16(13 12) = scaled sidev_z \ XX16(15 14) = scaled roofv_z \ XX16(17 16) = scaled nosev_z JSR LL51 \ Call LL51 to set XX12 to the dot products of XX15 and \ XX16, as follows: \ \ XX12(1 0) = [ x y z ] . [ sidev_x roofv_x nosev_x ] \ \ XX12(3 2) = [ x y z ] . [ sidev_y roofv_y nosev_y ] \ \ XX12(5 4) = [ x y z ] . [ sidev_z roofv_z nosev_z ] \ \ XX12 contains the vector from the ship's centre to \ the vertex, transformed from the orientation vector \ space to the universe orientated around our ship. So \ we can refer to this vector below, let's call it \ vertv, so: \ \ vertv_x = [ x y z ] . [ sidev_x roofv_x nosev_x ] \ \ vertv_y = [ x y z ] . [ sidev_y roofv_y nosev_y ] \ \ vertv_z = [ x y z ] . [ sidev_z roofv_z nosev_z ] \ \ To finish the calculation, we now want to calculate: \ \ vertv + [ x y z ] \ \ So let's start with the vertv_x + x LDA XX1+2 \ Set A = x_sign of the ship's location STA XX15+2 \ Set XX15+2 = x_sign EOR XX12+1 \ If the sign of x_sign * the sign of vertv_x is BMI LL52 \ negative (i.e. they have different signs), skip to \ LL52 CLC \ Set XX15(2 1 0) = XX1(2 1 0) + XX12(1 0) LDA XX12 \ = (x_sign x_hi x_lo) + vertv_x ADC XX1 \ STA XX15 \ Starting with the low bytes LDA XX1+1 \ And then doing the high bytes (we can add 0 here as ADC #0 \ we know the sign byte of vertv_x is 0) STA XX15+1 JMP LL53 \ We've added the x-coordinates, so jump to LL53 to do \ the y-coordinates .LL52 \ If we get here then x_sign and vertv_x have different \ signs, so we need to subtract them to get the result LDA XX1 \ Set XX15(2 1 0) = XX1(2 1 0) - XX12(1 0) SEC \ = (x_sign x_hi x_lo) - vertv_x SBC XX12 \ STA XX15 \ Starting with the low bytes LDA XX1+1 \ And then doing the high bytes (we can subtract 0 here SBC #0 \ as we know the sign byte of vertv_x is 0) STA XX15+1 BCS LL53 \ If the subtraction didn't underflow, then the sign of \ the result is the same sign as x_sign, and that's what \ we want, so we can jump down to LL53 to do the \ y-coordinates EOR #%11111111 \ Otherwise we need to negate the result using two's STA XX15+1 \ complement, so first we flip the bits of the high byte LDA #1 \ And then subtract the low byte from 1 SBC XX15 STA XX15 BCC P%+4 \ If the above subtraction underflowed then we need to INC XX15+1 \ bump the high byte of the result up by 1 LDA XX15+2 \ And now we flip the sign of the result to get the EOR #%10000000 \ correct result STA XX15+2 .LL53 \ Now for the y-coordinates, vertv_y + y LDA XX1+5 \ Set A = y_sign of the ship's location STA XX15+5 \ Set XX15+5 = y_sign EOR XX12+3 \ If the sign of y_sign * the sign of vertv_y is BMI LL54 \ negative (i.e. they have different signs), skip to \ LL54 CLC \ Set XX15(5 4 3) = XX1(5 4 3) + XX12(3 2) LDA XX12+2 \ = (y_sign y_hi y_lo) + vertv_y ADC XX1+3 \ STA XX15+3 \ Starting with the low bytes LDA XX1+4 \ And then doing the high bytes (we can add 0 here as ADC #0 \ we know the sign byte of vertv_y is 0) STA XX15+4 JMP LL55 \ We've added the y-coordinates, so jump to LL55 to do \ the z-coordinates .LL54 \ If we get here then y_sign and vertv_y have different \ signs, so we need to subtract them to get the result LDA XX1+3 \ Set XX15(5 4 3) = XX1(5 4 3) - XX12(3 2) SEC \ = (y_sign y_hi y_lo) - vertv_y SBC XX12+2 \ STA XX15+3 \ Starting with the low bytes LDA XX1+4 \ And then doing the high bytes (we can subtract 0 here SBC #0 \ as we know the sign byte of vertv_z is 0) STA XX15+4 BCS LL55 \ If the subtraction didn't underflow, then the sign of \ the result is the same sign as y_sign, and that's what \ we want, so we can jump down to LL55 to do the \ z-coordinates EOR #%11111111 \ Otherwise we need to negate the result using two's STA XX15+4 \ complement, so first we flip the bits of the high byte LDA XX15+3 \ And then flip the bits of the low byte and add 1 EOR #%11111111 ADC #1 STA XX15+3 LDA XX15+5 \ And now we flip the sign of the result to get the EOR #%10000000 \ correct result STA XX15+5 BCC LL55 \ If the above subtraction underflowed then we need to INC XX15+4 \ bump the high byte of the result up by 1 .LL55 \ Now for the z-coordinates, vertv_z + z LDA XX12+5 \ If vertv_z_hi is negative, jump down to LL56 BMI LL56 LDA XX12+4 \ Set (U T) = XX1(7 6) + XX12(5 4) CLC \ = (z_hi z_lo) + vertv_z ADC XX1+6 \ STA T \ Starting with the low bytes LDA XX1+7 \ And then doing the high bytes (we can add 0 here as ADC #0 \ we know the sign byte of vertv_y is 0) STA U JMP LL57 \ We've added the z-coordinates, so jump to LL57 \ The adding process is continued in part 7, after a \ couple of subroutines that we don't need quite yet