N6610 LCD 3D Demo Part II

Instead of drawing only the edges of a polyhedron, this time we draw the faces and 'fill' it with corresponding colors. This demo now uses a dsPIC (16-bit and 40MIPS core) for "faster" and "smoother" graphics in the N6610/N6100 LCD (w/ pcf8833 controller). See "lcd6610.h" for the used pinouts.



There are several ways of "hidden surface removal". The easiest way, and most appropriate for drawing convex polyhedron is the use of Backface culling. "Backface" will determine whether a surface (e.g. triangular face) is need to be drawn or not.
/-----------------------------------------------------------------------------------/
Draw3D routine:
/***** Draw 3D object with given vertices, triangular faces and angles of rotation******/ void draw_3D(Vertex * V, Triangle * T, nVertices, nTriangles, R) { // sin and cos values sinX = sin_table( R.x ) / 255.0; sinY = sin_table( R.y ) / 255.0; sinZ = sin_table( R.z ) / 255.0; cosX = cos_table( R.x ) / 255.0; cosY = cos_table( R.y ) / 255.0; cosZ = cos_table( R.z ) / 255.0; // calculate the new coordinates of points for (i=0; i< nVertices; i++) { tempX = V[i].x; tempY = V[i].y; tempZ = V[i].z; // store previous coordinates old_points[i] = new_points[i]; // rotation on X axis py = tempY * cosX - tempZ * sinX; pz = tempY * sinX + tempZ * cosX; tempY =py; tempZ = pz; // rotation on Z axis px = tempX * cosZ - tempY * sinZ; py = tempX * sinZ + tempY * cosZ; tempX = px; tempY = py; // rotation on Y axis px = tempX * cosY - tempZ * sinY; pz = tempX * sinY + tempZ * cosY; // save the screen coordinates new_points[i].x = px * SCALE_FACTOR + OFFSETX; new_points[i].y = py * SCALE_FACTOR + OFFSETY; } // erase previous triangles for (i=0; i< nTriangles; i++) { if( !Backface( old_points[T[i].A], old_points[T[i].B], old_points[T[i].C] ) ) fill_triangle(old_points[T[i].A], old_points[T[i].B], old_points[T[i].C], BG_COLOR); } // lcd plot new triangles for (i=0; i< nTriangles; i++) { if( !Backface( new_points[T[i].A], new_points[T[i].B], new_points[T[i].C] ) ) fill_triangle(new_points[T[i].A], new_points[T[i].B], new_points[T[i].C], T[i].color); } }

triangle color-fill routine:
void fill_triangle(Point A, Point B, Point C, color) { // bubble sort points if(B.y< A.y){ P=A; A=B; B=P; } if(C.y< B.y){ P=B; B=C; C=P; } if(C.y< A.y){ P=A; A=C; C=P; } if(B.y< A.y){ P=A; A=B; B=P; } // compute dx's dx1=0, dx2=0, dx3=0; if (B.y-A.y > 0) dx1 = (float)(B.x-A.x)/(B.y-A.y); if (C.y-B.y > 0) dx2 = (float)(C.x-B.x)/(C.y-B.y); if (C.y-A.y > 0) dx3 = (float)(C.x-A.x)/(C.y-A.y); for(h = (i16) A.y; h < B.y; h++) { sx = A.x + ((h - A.y) * dx3); ex = A.x + ((h - A.y) * dx1); draw_hline(sx,ex,h,color); } for(h = (i16) B.y; h < C.y; h++) { sx = A.x + ((h - A.y) * dx3); ex = B.x + ((h - B.y) * dx2); draw_hline(sx,ex,h,color); } }
(*another version of using dsPIC hardware multiplier/divider is included in the download)

detect whether a triangle is facing backward. /***** BACKFACE CULLING ******/ BOOL Backface(Point A, Point B, Point C) { Point L1, L2; // lines/edges L1.x = A.x - B.x; L1.y = A.y - B.y; L2.x = C.x - B.x; L2.y = C.y - B.y; if( ((L1.x * L2.y) - (L1.y * L2.x)) < 0 ) return TRUE; return FALSE; }


Complete MPLAB+C30 project (dsPIC33FJ16GS504):
n6610lcd_3D_demo_part2.zip

N6610 LCD 3D Demo

Nokia 6610/6100 LCD 3D projections demo using Microchip's PIC18F25J11. PIC18F25J11 is clocked at 12MHz external oscillator with 4xPLL enabled. It's operated at 3.3V supply, same with the LCD (and so, direct connections and higher spi clock rates are possible).

The demo is all about simple 3D projection - no rendering, no raycasting, etc., just the plotting of edges/lines. It displays common polyhedrons like tetrahedron, hexahedron(cube), octahedron, square pyramid, and triangular prism.

"3Ddemo.c"
/***** Draw 3D object with given vertices, edges and angles of rotation******/ void draw_3D(Vertex * V, Edge * E, nVertices, nEdges, xRot, yRot, zRot) { u8 i; float tempX,tempY,tempZ; // temporary coordinates float sinX,sinY,sinZ,cosX,cosY,cosZ; // precomputed sin and cos values float px,py,pz; // projected // sin and cos values sinX = sin_table( xRot ) / 255.0; sinY = sin_table( yRot ) / 255.0; sinZ = sin_table( zRot ) / 255.0; cosX = cos_table( xRot ) / 255.0; cosY = cos_table( yRot ) / 255.0; cosZ = cos_table( zRot ) / 255.0; // calculate the new coordinates of points for (i=0; i< nVertices; i++) { tempX = V[i].x; tempY = V[i].y; tempZ = V[i].z; // store previous coordinates old_points[i] = new_points[i]; // rotation on X axis py = tempY * cosX - tempZ * sinX; pz = tempY * sinX + tempZ * cosX; tempY =py; tempZ = pz; // rotation on Z axis px = tempX * cosZ - tempY * sinZ; py = tempX * sinZ + tempY * cosZ; tempX = px; tempY = py; // rotation on Y axis px = tempX * cosY - tempZ * sinY; pz = tempX * sinY + tempZ * cosY; // save the screen coordinates new_points[i].x = (u8)px * SCALE_FACTOR + OFFSETX; new_points[i].y = (u8)py * SCALE_FACTOR + OFFSETY; } // lcd plot for (i=0; i< nEdges; i++) { // erase old edges drawline( old_points[E[i].start].x, old_points[E[i].start].y, old_points[E[i].end].x, old_points[E[i].end].y, BG_COLOR); // draw new edges drawline( new_points[E[i].start].x, new_points[E[i].start].y, new_points[E[i].end].x, new_points[E[i].end].y, LINE_COLOR); }
*based on original sources:
Nokia 6100 LCD with CCS C
3D Vector objects in C using the PIC micro

Microchip C18 project:  n6610lcd_3D_demo.zip