solvespace/solvespace.cpp

//-----------------------------------------------------------------------------
// Entry point in to the program, our registry-stored settings and top-level
// housekeeping when we open, save, and create new files.
//
// Copyright 2008-2013 Jonathan Westhues.
//-----------------------------------------------------------------------------
#include "solvespace.h"

SolveSpace SS;
Sketch SK;

void SolveSpace::Init(char *cmdLine) {
    SS.tangentArcRadius = 10.0;

    // Then, load the registry settings.
    int i;
    // Default list of colors for the model material
    modelColor[0] = CnfThawDWORD(RGB(150, 150, 150), "ModelColor_0");
    modelColor[1] = CnfThawDWORD(RGB(100, 100, 100), "ModelColor_1");
    modelColor[2] = CnfThawDWORD(RGB( 30,  30,  30), "ModelColor_2");
    modelColor[3] = CnfThawDWORD(RGB(150,   0,   0), "ModelColor_3");
    modelColor[4] = CnfThawDWORD(RGB(  0, 100,   0), "ModelColor_4");
    modelColor[5] = CnfThawDWORD(RGB(  0,  80,  80), "ModelColor_5");
    modelColor[6] = CnfThawDWORD(RGB(  0,   0, 130), "ModelColor_6");
    modelColor[7] = CnfThawDWORD(RGB( 80,   0,  80), "ModelColor_7");
    // Light intensities
    lightIntensity[0] = CnfThawFloat(1.0f, "LightIntensity_0");
    lightIntensity[1] = CnfThawFloat(0.5f, "LightIntensity_1");
    ambientIntensity = 0.3; // no setting for that yet
    // Light positions
    lightDir[0].x = CnfThawFloat(-1.0f, "LightDir_0_Right"     );
    lightDir[0].y = CnfThawFloat( 1.0f, "LightDir_0_Up"        );
    lightDir[0].z = CnfThawFloat( 0.0f, "LightDir_0_Forward"   );
    lightDir[1].x = CnfThawFloat( 1.0f, "LightDir_1_Right"     );
    lightDir[1].y = CnfThawFloat( 0.0f, "LightDir_1_Up"        );
    lightDir[1].z = CnfThawFloat( 0.0f, "LightDir_1_Forward"   );
    // Chord tolerance
    chordTol = CnfThawFloat(2.0f, "ChordTolerance");
    // Max pwl segments to generate
    maxSegments = CnfThawDWORD(10, "MaxSegments");
    // View units
    viewUnits = (Unit)CnfThawDWORD((DWORD)UNIT_MM, "ViewUnits");
    // Number of digits after the decimal point
    afterDecimalMm = CnfThawDWORD(2, "AfterDecimalMm");
    afterDecimalInch = CnfThawDWORD(3, "AfterDecimalInch");
    // Camera tangent (determines perspective)
    cameraTangent = CnfThawFloat(0.3f/1e3f, "CameraTangent");
    // Grid spacing
    gridSpacing = CnfThawFloat(5.0f, "GridSpacing");
    // Export scale factor
    exportScale = CnfThawFloat(1.0f, "ExportScale");
    // Export offset (cutter radius comp)
    exportOffset = CnfThawFloat(0.0f, "ExportOffset");
    // Rewrite exported colors close to white into black (assuming white bg)
    fixExportColors = CnfThawDWORD(1, "FixExportColors");
    // Draw back faces of triangles (when mesh is leaky/self-intersecting)
    drawBackFaces = CnfThawDWORD(1, "DrawBackFaces");
    // Check that contours are closed and not self-intersecting
    checkClosedContour = CnfThawDWORD(1, "CheckClosedContour");
    // Export shaded triangles in a 2d view
    exportShadedTriangles = CnfThawDWORD(1, "ExportShadedTriangles");
    // Export pwl curves (instead of exact) always
    exportPwlCurves = CnfThawDWORD(0, "ExportPwlCurves");
    // Background color on-screen
    backgroundColor = CnfThawDWORD(RGB(0, 0, 0), "BackgroundColor");
    // Whether export canvas size is fixed or derived from bbox
    exportCanvasSizeAuto = CnfThawDWORD(1, "ExportCanvasSizeAuto");
    // Margins for automatic canvas size
    exportMargin.left   = CnfThawFloat(5.0f, "ExportMargin_Left");
    exportMargin.right  = CnfThawFloat(5.0f, "ExportMargin_Right");
    exportMargin.bottom = CnfThawFloat(5.0f, "ExportMargin_Bottom");
    exportMargin.top    = CnfThawFloat(5.0f, "ExportMargin_Top");
    // Dimensions for fixed canvas size
    exportCanvas.width  = CnfThawFloat(100.0f, "ExportCanvas_Width");
    exportCanvas.height = CnfThawFloat(100.0f, "ExportCanvas_Height");
    exportCanvas.dx     = CnfThawFloat(  5.0f, "ExportCanvas_Dx");
    exportCanvas.dy     = CnfThawFloat(  5.0f, "ExportCanvas_Dy");
    // Extra parameters when exporting G code
    gCode.depth         = CnfThawFloat(10.0f, "GCode_Depth");
    gCode.passes        = CnfThawDWORD(1, "GCode_Passes");
    gCode.feed          = CnfThawFloat(10.0f, "GCode_Feed");
    gCode.plungeFeed    = CnfThawFloat(10.0f, "GCode_PlungeFeed");
    // Show toolbar in the graphics window
    showToolbar = CnfThawDWORD(1, "ShowToolbar");
    // Recent files menus
    for(i = 0; i < MAX_RECENT; i++) {
        char name[100];
        sprintf(name, "RecentFile_%d", i);
        strcpy(RecentFile[i], "");
        CnfThawString(RecentFile[i], MAX_PATH, name);
    }
    RefreshRecentMenus();

    // The default styles (colors, line widths, etc.) are also stored in the
    // configuration file, but we will automatically load those as we need
    // them.

    // Start with either an empty file, or the file specified on the
    // command line.
    NewFile();
    AfterNewFile();
    if(strlen(cmdLine) != 0) {
        if(LoadFromFile(cmdLine)) {
            strcpy(saveFile, cmdLine);
        } else {
            NewFile();
        }
    }
    AfterNewFile();
}

void SolveSpace::Exit(void) {
    int i;
    char name[100];
    // Recent files
    for(i = 0; i < MAX_RECENT; i++) {
        sprintf(name, "RecentFile_%d", i);
        CnfFreezeString(RecentFile[i], name);
    }
    // Model colors
    for(i = 0; i < MODEL_COLORS; i++) {
        sprintf(name, "ModelColor_%d", i);
        CnfFreezeDWORD(modelColor[i], name);
    }
    // Light intensities
    CnfFreezeFloat((float)lightIntensity[0], "LightIntensity_0");
    CnfFreezeFloat((float)lightIntensity[1], "LightIntensity_1");
    // Light directions
    CnfFreezeFloat((float)lightDir[0].x, "LightDir_0_Right");
    CnfFreezeFloat((float)lightDir[0].y, "LightDir_0_Up");
    CnfFreezeFloat((float)lightDir[0].z, "LightDir_0_Forward");
    CnfFreezeFloat((float)lightDir[1].x, "LightDir_1_Right");
    CnfFreezeFloat((float)lightDir[1].y, "LightDir_1_Up");
    CnfFreezeFloat((float)lightDir[1].z, "LightDir_1_Forward");
    // Chord tolerance
    CnfFreezeFloat((float)chordTol, "ChordTolerance");
    // Max pwl segments to generate
    CnfFreezeDWORD((DWORD)maxSegments, "MaxSegments");
    // View units
    CnfFreezeDWORD((DWORD)viewUnits, "ViewUnits");
    // Number of digits after the decimal point
    CnfFreezeDWORD((DWORD)afterDecimalMm, "AfterDecimalMm");
    CnfFreezeDWORD((DWORD)afterDecimalInch, "AfterDecimalInch");
    // Camera tangent (determines perspective)
    CnfFreezeFloat((float)cameraTangent, "CameraTangent");
    // Grid spacing
    CnfFreezeFloat(gridSpacing, "GridSpacing");
    // Export scale (a float, stored as a DWORD)
    CnfFreezeFloat(exportScale, "ExportScale");
    // Export offset (cutter radius comp)
    CnfFreezeFloat(exportOffset, "ExportOffset");
    // Rewrite exported colors close to white into black (assuming white bg)
    CnfFreezeDWORD(fixExportColors, "FixExportColors");
    // Draw back faces of triangles (when mesh is leaky/self-intersecting)
    CnfFreezeDWORD(drawBackFaces, "DrawBackFaces");
    // Check that contours are closed and not self-intersecting
    CnfFreezeDWORD(checkClosedContour, "CheckClosedContour");
    // Export shaded triangles in a 2d view
    CnfFreezeDWORD(exportShadedTriangles, "ExportShadedTriangles");
    // Export pwl curves (instead of exact) always
    CnfFreezeDWORD(exportPwlCurves, "ExportPwlCurves");
    // Background color on-screen
    CnfFreezeDWORD(backgroundColor, "BackgroundColor");
    // Whether export canvas size is fixed or derived from bbox
    CnfFreezeDWORD(exportCanvasSizeAuto, "ExportCanvasSizeAuto");
    // Margins for automatic canvas size
    CnfFreezeFloat(exportMargin.left,   "ExportMargin_Left");
    CnfFreezeFloat(exportMargin.right,  "ExportMargin_Right");
    CnfFreezeFloat(exportMargin.bottom, "ExportMargin_Bottom");
    CnfFreezeFloat(exportMargin.top,    "ExportMargin_Top");
    // Dimensions for fixed canvas size
    CnfFreezeFloat(exportCanvas.width,  "ExportCanvas_Width");
    CnfFreezeFloat(exportCanvas.height, "ExportCanvas_Height");
    CnfFreezeFloat(exportCanvas.dx,     "ExportCanvas_Dx");
    CnfFreezeFloat(exportCanvas.dy,     "ExportCanvas_Dy");
     // Extra parameters when exporting G code
    CnfFreezeFloat(gCode.depth,         "GCode_Depth");
    CnfFreezeDWORD(gCode.passes,        "GCode_Passes");
    CnfFreezeFloat(gCode.feed,          "GCode_Feed");
    CnfFreezeFloat(gCode.plungeFeed,    "GCode_PlungeFeed");
    // Show toolbar in the graphics window
    CnfFreezeDWORD(showToolbar, "ShowToolbar");

    // And the default styles, colors and line widths and such.
    Style::FreezeDefaultStyles();

    ExitNow();
}

void SolveSpace::DoLater(void) {
    if(later.generateAll) GenerateAll();
    if(later.showTW) TW.Show();
    ZERO(&later);
}

double SolveSpace::MmPerUnit(void) {
    if(viewUnits == UNIT_INCHES) {
        return 25.4;
    } else {
        return 1.0;
    }
}
const char *SolveSpace::UnitName(void) {
    if(viewUnits == UNIT_INCHES) {
        return "inch";
    } else {
        return "mm";
    }
}
char *SolveSpace::MmToString(double v) {
    static int WhichBuf;
    static char Bufs[8][128];
    char fmt[128];

    WhichBuf++;
    if(WhichBuf >= 8 || WhichBuf < 0) WhichBuf = 0;

    char *s = Bufs[WhichBuf];
    if(viewUnits == UNIT_INCHES) {
        sprintf(fmt, "%%.%df", afterDecimalInch);
        sprintf(s, fmt, v/25.4);
    } else {
        sprintf(fmt, "%%.%df", afterDecimalMm);
        sprintf(s, fmt, v);
    }
    return s;
}
double SolveSpace::ExprToMm(Expr *e) {
    return (e->Eval()) * MmPerUnit();
}
double SolveSpace::StringToMm(const char *str) {
    return atof(str) * MmPerUnit();
}
double SolveSpace::ChordTolMm(void) {
    return SS.chordTol / SS.GW.scale;
}
int SolveSpace::UnitDigitsAfterDecimal(void) {
    return (viewUnits == UNIT_INCHES) ? afterDecimalInch : afterDecimalMm;
}
void SolveSpace::SetUnitDigitsAfterDecimal(int v) {
    if(viewUnits == UNIT_INCHES) {
        afterDecimalInch = v;
    } else {
        afterDecimalMm = v;
    }
}

double SolveSpace::CameraTangent(void) {
    if(!usePerspectiveProj) {
        return 0;
    } else {
        return cameraTangent;
    }
}

void SolveSpace::AfterNewFile(void) {
    // Clear out the traced point, which is no longer valid
    traced.point = Entity::NO_ENTITY;
    traced.path.l.Clear();
    // and the naked edges
    nakedEdges.Clear();

    // GenerateAll() expects the view to be valid, because it uses that to
    // fill in default values for extrusion depths etc. (which won't matter
    // here, but just don't let it work on garbage)
    SS.GW.offset    = Vector::From(0, 0, 0);
    SS.GW.projRight = Vector::From(1, 0, 0);
    SS.GW.projUp    = Vector::From(0, 1, 0);

    ReloadAllImported();
    GenerateAll(-1, -1);

    TW.Init();
    GW.Init();

    unsaved = false;

    int w, h;
    GetGraphicsWindowSize(&w, &h);
    GW.width = w;
    GW.height = h;

    // The triangles haven't been generated yet, but zoom to fit the entities
    // roughly in the window, since that sets the mesh tolerance. Consider
    // invisible entities, so we still get something reasonable if the only
    // thing visible is the not-yet-generated surfaces.
    GW.ZoomToFit(true);

    GenerateAll(0, INT_MAX);
    later.showTW = true;
    // Then zoom to fit again, to fit the triangles
    GW.ZoomToFit(false);

    // Create all the default styles; they'll get created on the fly anyways,
    // but can't hurt to do it now.
    Style::CreateAllDefaultStyles();

    UpdateWindowTitle();
}

void SolveSpace::RemoveFromRecentList(char *file) {
    int src, dest;
    dest = 0;
    for(src = 0; src < MAX_RECENT; src++) {
        if(strcmp(file, RecentFile[src]) != 0) {
            if(src != dest) strcpy(RecentFile[dest], RecentFile[src]);
            dest++;
        }
    }
    while(dest < MAX_RECENT) strcpy(RecentFile[dest++], "");
    RefreshRecentMenus();
}
void SolveSpace::AddToRecentList(char *file) {
    RemoveFromRecentList(file);

    int src;
    for(src = MAX_RECENT - 2; src >= 0; src--) {
        strcpy(RecentFile[src+1], RecentFile[src]);
    }
    strcpy(RecentFile[0], file);
    RefreshRecentMenus();
}

bool SolveSpace::GetFilenameAndSave(bool saveAs) {

    char newFile[MAX_PATH];
    strcpy(newFile, saveFile);
    if(saveAs || strlen(newFile)==0) {
        if(!GetSaveFile(newFile, SLVS_EXT, SLVS_PATTERN)) return false;
    }

    if(SaveToFile(newFile)) {
        AddToRecentList(newFile);
        strcpy(saveFile, newFile);
        unsaved = false;
        return true;
    } else {
        return false;
    }
}

bool SolveSpace::OkayToStartNewFile(void) {
    if(!unsaved) return true;

    switch(SaveFileYesNoCancel()) {
        case IDYES:
            return GetFilenameAndSave(false);

        case IDNO:
            return true;

        case IDCANCEL:
            return false;
        
        default: oops();
    }
}

void SolveSpace::UpdateWindowTitle(void) {
    if(strlen(saveFile) == 0) {
        SetWindowTitle("SolveSpace - (not yet saved)");
    } else {
        char buf[MAX_PATH+100];
        sprintf(buf, "SolveSpace - %s", saveFile);
        SetWindowTitle(buf);
    }
}

void SolveSpace::MenuFile(int id) {
    if(id >= RECENT_OPEN && id < (RECENT_OPEN+MAX_RECENT)) {
        if(!SS.OkayToStartNewFile()) return;

        char newFile[MAX_PATH];
        strcpy(newFile, RecentFile[id-RECENT_OPEN]);
        RemoveFromRecentList(newFile);
        if(SS.LoadFromFile(newFile)) {
            strcpy(SS.saveFile, newFile);
            AddToRecentList(newFile);
        } else {
            strcpy(SS.saveFile, "");
            SS.NewFile();
        }
        SS.AfterNewFile();
        return;
    }

    switch(id) {
        case GraphicsWindow::MNU_NEW:
            if(!SS.OkayToStartNewFile()) break;

            strcpy(SS.saveFile, "");
            SS.NewFile();
            SS.AfterNewFile();
            break;

        case GraphicsWindow::MNU_OPEN: {
            if(!SS.OkayToStartNewFile()) break;

            char newFile[MAX_PATH] = "";
            if(GetOpenFile(newFile, SLVS_EXT, SLVS_PATTERN)) {
                if(SS.LoadFromFile(newFile)) {
                    strcpy(SS.saveFile, newFile);
                    AddToRecentList(newFile);
                } else {
                    strcpy(SS.saveFile, "");
                    SS.NewFile();
                }
                SS.AfterNewFile();
            }
            break;
        }

        case GraphicsWindow::MNU_SAVE:
            SS.GetFilenameAndSave(false);
            break;

        case GraphicsWindow::MNU_SAVE_AS:
            SS.GetFilenameAndSave(true);
            break;

        case GraphicsWindow::MNU_EXPORT_PNG: {
            char exportFile[MAX_PATH] = "";
            if(!GetSaveFile(exportFile, PNG_EXT, PNG_PATTERN)) break;
            SS.ExportAsPngTo(exportFile); 
            break;
        }

        case GraphicsWindow::MNU_EXPORT_VIEW: {
            char exportFile[MAX_PATH] = "";
            if(!GetSaveFile(exportFile, VEC_EXT, VEC_PATTERN)) break;

            // If the user is exporting something where it would be
            // inappropriate to include the constraints, then warn.
            if(SS.GW.showConstraints &&
                (StringEndsIn(exportFile, ".txt") ||
                 fabs(SS.exportOffset) > LENGTH_EPS))
            {
                Message("Constraints are currently shown, and will be exported "
                        "in the toolpath. This is probably not what you want; "
                        "hide them by clicking the link at the top of the "
                        "text window.");
            }

            SS.ExportViewOrWireframeTo(exportFile, false); 
            break;
        }

        case GraphicsWindow::MNU_EXPORT_WIREFRAME: {
            char exportFile[MAX_PATH] = "";
            if(!GetSaveFile(exportFile, V3D_EXT, V3D_PATTERN)) break;
            SS.ExportViewOrWireframeTo(exportFile, true); 
            break;
        }

        case GraphicsWindow::MNU_EXPORT_SECTION: {
            char exportFile[MAX_PATH] = "";
            if(!GetSaveFile(exportFile, VEC_EXT, VEC_PATTERN)) break;
            SS.ExportSectionTo(exportFile); 
            break;
        }

        case GraphicsWindow::MNU_EXPORT_MESH: {
            char exportFile[MAX_PATH] = "";
            if(!GetSaveFile(exportFile, MESH_EXT, MESH_PATTERN)) break;
            SS.ExportMeshTo(exportFile); 
            break;
        }

        case GraphicsWindow::MNU_EXPORT_SURFACES: {
            char exportFile[MAX_PATH] = "";
            if(!GetSaveFile(exportFile, SRF_EXT, SRF_PATTERN)) break;
            StepFileWriter sfw;
            ZERO(&sfw);
            sfw.ExportSurfacesTo(exportFile); 
            break;
        }

        case GraphicsWindow::MNU_EXIT:
            if(!SS.OkayToStartNewFile()) break;
            SS.Exit();
            break;

        default: oops();
    }

    SS.UpdateWindowTitle();
}

void SolveSpace::MenuAnalyze(int id) {
    SS.GW.GroupSelection();
#define gs (SS.GW.gs)

    switch(id) {
        case GraphicsWindow::MNU_STEP_DIM:
            if(gs.constraints == 1 && gs.n == 0) {
                Constraint *c = SK.GetConstraint(gs.constraint[0]);
                if(c->HasLabel() && !c->reference) {
                    SS.TW.shown.dimFinish = c->valA;
                    SS.TW.shown.dimSteps = 10;
                    SS.TW.shown.dimIsDistance =
                        (c->type != Constraint::ANGLE) &&
                        (c->type != Constraint::LENGTH_RATIO);
                    SS.TW.shown.constraint = c->h;
                    SS.TW.shown.screen = TextWindow::SCREEN_STEP_DIMENSION;

                    // The step params are specified in the text window,
                    // so force that to be shown.
                    SS.GW.ForceTextWindowShown();

                    SS.later.showTW = true;
                    SS.GW.ClearSelection();
                } else {
                    Error("Constraint must have a label, and must not be "
                          "a reference dimension.");
                }
            } else {
                Error("Bad selection for step dimension; select a constraint.");
            }
            break;

        case GraphicsWindow::MNU_NAKED_EDGES: {
            SS.nakedEdges.Clear();

            Group *g = SK.GetGroup(SS.GW.activeGroup);
            SMesh *m = &(g->displayMesh);
            SKdNode *root = SKdNode::From(m);
            bool inters, leaks;
            root->MakeCertainEdgesInto(&(SS.nakedEdges), 
                SKdNode::NAKED_OR_SELF_INTER_EDGES, true, &inters, &leaks);

            InvalidateGraphics();

            const char *intersMsg = inters ?
                "The mesh is self-intersecting (NOT okay, invalid)." :
                "The mesh is not self-intersecting (okay, valid).";
            const char *leaksMsg = leaks ?
                "The mesh has naked edges (NOT okay, invalid)." :
                "The mesh is watertight (okay, valid).";

            char cntMsg[1024];
            sprintf(cntMsg, "\n\nThe model contains %d triangles, from "
                            "%d surfaces.",
                g->displayMesh.l.n, g->runningShell.surface.n);

            if(SS.nakedEdges.l.n == 0) {
                Message("%s\n\n%s\n\nZero problematic edges, good.%s",
                    intersMsg, leaksMsg, cntMsg);
            } else {
                Error("%s\n\n%s\n\n%d problematic edges, bad.%s",
                    intersMsg, leaksMsg, SS.nakedEdges.l.n, cntMsg);
            }
            break;
        }

        case GraphicsWindow::MNU_INTERFERENCE: {
            SS.nakedEdges.Clear();

            SMesh *m = &(SK.GetGroup(SS.GW.activeGroup)->displayMesh);
            SKdNode *root = SKdNode::From(m);
            bool inters, leaks;
            root->MakeCertainEdgesInto(&(SS.nakedEdges),
                SKdNode::SELF_INTER_EDGES, false, &inters, &leaks);

            InvalidateGraphics();

            if(inters) {
                Error("%d edges interfere with other triangles, bad.",
                    SS.nakedEdges.l.n);
            } else {
                Message("The assembly does not interfere, good.");
            }
            break;
        }

        case GraphicsWindow::MNU_VOLUME: {
            SMesh *m = &(SK.GetGroup(SS.GW.activeGroup)->displayMesh);
           
            double vol = 0;
            int i;
            for(i = 0; i < m->l.n; i++) {
                STriangle tr = m->l.elem[i];

                // Translate to place vertex A at (x, y, 0)
                Vector trans = Vector::From(tr.a.x, tr.a.y, 0);
                tr.a = (tr.a).Minus(trans);
                tr.b = (tr.b).Minus(trans);
                tr.c = (tr.c).Minus(trans);

                // Rotate to place vertex B on the y-axis. Depending on
                // whether the triangle is CW or CCW, C is either to the
                // right or to the left of the y-axis. This handles the
                // sign of our normal.
                Vector u = Vector::From(-tr.b.y, tr.b.x, 0);
                u = u.WithMagnitude(1);
                Vector v = Vector::From(tr.b.x, tr.b.y, 0);
                v = v.WithMagnitude(1);
                Vector n = Vector::From(0, 0, 1);

                tr.a = (tr.a).DotInToCsys(u, v, n);
                tr.b = (tr.b).DotInToCsys(u, v, n);
                tr.c = (tr.c).DotInToCsys(u, v, n);

                n = tr.Normal().WithMagnitude(1);

                // Triangles on edge don't contribute
                if(fabs(n.z) < LENGTH_EPS) continue;
               
                // The plane has equation p dot n = a dot n
                double d = (tr.a).Dot(n);
                // nx*x + ny*y + nz*z = d
                // nz*z = d - nx*x - ny*y
                double A = -n.x/n.z, B = -n.y/n.z, C = d/n.z;

                double mac = tr.c.y/tr.c.x, mbc = (tr.c.y - tr.b.y)/tr.c.x;
                double xc = tr.c.x, yb = tr.b.y;
               
                // I asked Maple for
                //    int(int(A*x + B*y +C, y=mac*x..(mbc*x + yb)), x=0..xc);
                double integral = 
                    (1.0/3)*(
                        A*(mbc-mac)+
                        (1.0/2)*B*(mbc*mbc-mac*mac)
                    )*(xc*xc*xc)+
                    (1.0/2)*(A*yb+B*yb*mbc+C*(mbc-mac))*xc*xc+
                    C*yb*xc+
                    (1.0/2)*B*yb*yb*xc;

                vol += integral;
            }

            char msg[1024];
            sprintf(msg, "The volume of the solid model is:\n\n"
                         "    %.3f %s^3",
                vol / pow(SS.MmPerUnit(), 3),
                SS.UnitName());

            if(SS.viewUnits == SolveSpace::UNIT_MM) {
                sprintf(msg+strlen(msg), "\n    %.2f mL", vol/(10*10*10));
            }
            strcpy(msg+strlen(msg),
                "\n\nCurved surfaces have been approximated as triangles.\n"
                "This introduces error, typically of around 1%.");
            Message("%s", msg);
            break;
        }

        case GraphicsWindow::MNU_AREA: {
            Group *g = SK.GetGroup(SS.GW.activeGroup);
            if(g->polyError.how != Group::POLY_GOOD) {
                Error("This group does not contain a correctly-formed "
                      "2d closed area. It is open, not coplanar, or self-"
                      "intersecting.");
                break;
            }
            SEdgeList sel;
            ZERO(&sel);
            g->polyLoops.MakeEdgesInto(&sel);
            SPolygon sp;
            ZERO(&sp);
            sel.AssemblePolygon(&sp, NULL, true);
            sp.normal = sp.ComputeNormal();
            sp.FixContourDirections();
            double area = sp.SignedArea();
            double scale = SS.MmPerUnit();
            Message("The area of the region sketched in this group is:\n\n"
                    "    %.3f %s^2\n\n"
                    "Curves have been approximated as piecewise linear.\n"
                    "This introduces error, typically of around 1%%.",
                area / (scale*scale),
                SS.UnitName());
            sel.Clear();
            sp.Clear();
            break;
        }

        case GraphicsWindow::MNU_SHOW_DOF:
            // This works like a normal solve, except that it calculates
            // which variables are free/bound at the same time.
            SS.GenerateAll(0, INT_MAX, true);
            break;

        case GraphicsWindow::MNU_TRACE_PT:
            if(gs.points == 1 && gs.n == 1) {
                SS.traced.point = gs.point[0];
                SS.GW.ClearSelection();
            } else {
                Error("Bad selection for trace; select a single point.");
            }
            break;
            
        case GraphicsWindow::MNU_STOP_TRACING: {
            char exportFile[MAX_PATH] = "";
            if(GetSaveFile(exportFile, CSV_EXT, CSV_PATTERN)) {
                FILE *f = fopen(exportFile, "wb");
                if(f) {
                    int i;
                    SContour *sc = &(SS.traced.path);
                    for(i = 0; i < sc->l.n; i++) {
                        Vector p = sc->l.elem[i].p;
                        double s = SS.exportScale;
                        fprintf(f, "%.10f, %.10f, %.10f\r\n",
                            p.x/s, p.y/s, p.z/s);
                    }
                    fclose(f);
                } else {
                    Error("Couldn't write to '%s'", exportFile);
                }
            }
            // Clear the trace, and stop tracing
            SS.traced.point = Entity::NO_ENTITY;
            SS.traced.path.l.Clear();
            InvalidateGraphics();
            break;
        }

        default: oops();
    }
}

void SolveSpace::MenuHelp(int id) {
    switch(id) {
        case GraphicsWindow::MNU_WEBSITE:
            OpenWebsite("http://solvespace.com/helpmenu");
            break;
        
        case GraphicsWindow::MNU_ABOUT:
            Message("This is SolveSpace version 2.0.\n\n"
                "For more information, see http://solvespace.com/\n\n"
                "Built " __TIME__ " " __DATE__ ".\n\n"
                "Copyright 2008-2013 Jonathan Westhues.\n"
                "All Rights Reserved.");
            break;

        default: oops();
    }
}