Related
I couldn't solve the problem myself, even reading answers to related questions (I already searched in stackoverflow, but I couldn't understand the proposed solutions or adapt them to my case).
This is the code the draws the grid:
// global variables
int cameraOffsetX = SCREEN_WIDTH / 2; //x coordinate of the "origin"
int cameraOffsetY = SCREEN_HEIGHT / 2;
int cameraZoomSpriteSize = 32; //size of a square in the current zoom
float zoomFactor = 1;
--------------------
//grid
SDL_SetRenderDrawColor(renderer, 0xe6, 0xe6, 0xe6, SDL_ALPHA_OPAQUE);
for (int i = cameraOffsetX - cameraOffsetX / cameraZoomSpriteSize * cameraZoomSpriteSize;
i < window_width; i += cameraZoomSpriteSize)
SDL_RenderDrawLine(renderer, i, 0, i, window_height);
for (int i = cameraOffsetY - cameraOffsetY / cameraZoomSpriteSize * cameraZoomSpriteSize;
i < window_height; i += cameraZoomSpriteSize)
SDL_RenderDrawLine(renderer, 0, i, window_width, i);
//origin
SDL_SetRenderDrawColor(renderer, 0xff, 0, 0, SDL_ALPHA_OPAQUE);
SDL_RenderDrawLine(renderer, cameraOffsetX, cameraOffsetY - cameraZoomSpriteSize, cameraOffsetX,
cameraOffsetY + cameraZoomSpriteSize);
SDL_RenderDrawLine(renderer, cameraOffsetX - cameraZoomSpriteSize, cameraOffsetY,
cameraOffsetX + cameraZoomSpriteSize, cameraOffsetY);
and this is the code that attempts to obtain the wanted behaviour which isn't quite right yet:
case SDL_MOUSEWHEEL:
int mx, my;
SDL_GetMouseState(&mx, &my);
if (event.wheel.y > 0) // scroll up
{
if (cameraZoomSpriteSize < 64) {
cameraOffsetX-=(mx-cameraOffsetX)*4/cameraZoomSpriteSize+(mx-cameraOffsetX)%cameraZoomSpriteSize*4/cameraZoomSpriteSize;
cameraOffsetY-=(my-cameraOffsetY)*4/cameraZoomSpriteSize+(my-cameraOffsetY)%cameraZoomSpriteSize*4/cameraZoomSpriteSize;
cameraZoomSpriteSize += 4;
zoomFactor += 0.125;
}
} else if (event.wheel.y < 0) // scroll down
{
if (cameraZoomSpriteSize > 4) {
cameraOffsetX+=(mx-cameraOffsetX)*4/cameraZoomSpriteSize+(mx-cameraOffsetX)%cameraZoomSpriteSize*4/cameraZoomSpriteSize;
cameraOffsetY+=(my-cameraOffsetY)*4/cameraZoomSpriteSize+(my-cameraOffsetY)%cameraZoomSpriteSize*4/cameraZoomSpriteSize;
cameraZoomSpriteSize -= 4;
zoomFactor -= 0.125;
}
}
break;
What are the correct formula for cameraOffsetX and cameraOffsetY. Unfortunately I couldn't visualize the math.
General principle:
cameraOffsetX = mx + (cameraOffsetX - mx) * newZoomCoefficient / oldZoomCoefficient
The solution I read here was right; only I couldn't translate right away zoompointX and scalechange.
I drew segments on a piece of paper and tried to scale them to figure out the same exact formula of that post.
case SDL_MOUSEWHEEL:
int mx, my;
SDL_GetMouseState(&mx, &my);
if (event.wheel.y > 0) // scroll up
{
if (cameraZoomSpriteSize < 64) {
cameraOffsetX-=(mx-cameraOffsetX)*4/cameraZoomSpriteSize;
cameraOffsetY-=(my-cameraOffsetY)*4/cameraZoomSpriteSize;
cameraZoomSpriteSize += 4;
zoomFactor += 0.125;
}
} else if (event.wheel.y < 0) // scroll down
{
if (cameraZoomSpriteSize > 4) {
cameraOffsetX+=(mx-cameraOffsetX)*4/cameraZoomSpriteSize;
cameraOffsetY+=(my-cameraOffsetY)*4/cameraZoomSpriteSize;
cameraZoomSpriteSize -= 4;
zoomFactor -= 0.125;
}
}
break;
This problem took me half of yesterday and this morning to solve :(
I am trying to convert an SVG arc to a series of line segments. The background is, that I want to draw an arc using (reportlab)[http://www.reportlab.com/].
The svg gives me these parameters (accoring to here).
rx,ry,x-axis-rotation,large-arc-flag,sweep-flag,dx,dy
Now I need to determine lines following this arcs. But I do not understand how I can convert this to something geometrical more usable.
How would I determine the center of the ellipse arc and its rotation?
SVG elliptic arcs are really tricky and took me a while to implement it (even following the SVG specs). I ended up with something like this in C++:
//---------------------------------------------------------------------------
class svg_usek // virtual class for svg_line types
{
public:
int pat; // svg::pat[] index
virtual void reset(){};
virtual double getl (double mx,double my){ return 1.0; };
virtual double getdt(double dl,double mx,double my){ return 0.1; };
virtual void getpnt(double &x,double &y,double t){};
virtual void compute(){};
virtual void getcfg(AnsiString &nam,AnsiString &dtp,AnsiString &val){};
virtual void setcfg(AnsiString &nam,AnsiString &dtp,AnsiString &val,int &an,int &ad,int &av){};
};
//---------------------------------------------------------------------------
class svg_ela:public svg_usek // sweep = 0 arc goes from line p0->p1 CW
{ // sweep = 1 arc goes from line p0->p1 CCW
public: // larc is unused if |da|=PI
double x0,y0,x1,y1,a,b,alfa; int sweep,larc;
double sx,sy,a0,a1,da,ang; // sx,sy rotated center by ang
double cx,cy; // real center
void reset() { x0=0; y0=0; x1=0; y1=0; a=0; b=0; alfa=0; sweep=false; larc=false; compute(); }
double getl (double mx,double my);
// double getdt(double dl,double mx,double my);
double getdt(double dl,double mx,double my) { int n; double dt; dt=divide(dl,getl(mx,my)); n=floor(divide(1.0,dt)); if (n<1) n=1; return divide(1.0,n); }
void getpnt(double &x,double &y,double t);
void compute();
void getcfg(AnsiString &nam,AnsiString &dtp,AnsiString &val);
void setcfg(AnsiString &nam,AnsiString &dtp,AnsiString &val,int &an,int &ad,int &av);
svg_ela() {}
svg_ela(svg_ela& a) { *this=a; }
~svg_ela() {}
svg_ela* operator = (const svg_ela *a) { *this=*a; return this; }
//svg_ela* operator = (const svg_ela &a) { ...copy... return this; }
};
//---------------------------------------------------------------------------
void svg_ela::getpnt(double &x,double &y,double t)
{
double c,s,xx,yy;
t=a0+(da*t);
xx=sx+a*cos(t);
yy=sy+b*sin(t);
c=cos(-ang);
s=sin(-ang);
x=xx*c-yy*s;
y=xx*s+yy*c;
}
//---------------------------------------------------------------------------
void svg_ela::compute()
{
double ax,ay,bx,by; // body
double vx,vy,l,db;
int _sweep;
double c,s,e;
ang=pi-alfa;
_sweep=sweep;
if (larc) _sweep=!_sweep;
e=divide(a,b);
c=cos(ang);
s=sin(ang);
ax=x0*c-y0*s;
ay=x0*s+y0*c;
bx=x1*c-y1*s;
by=x1*s+y1*c;
ay*=e; // transform to circle
by*=e;
sx=0.5*(ax+bx); // mid point between A,B
sy=0.5*(ay+by);
vx=(ay-by);
vy=(bx-ax);
l=divide(a*a,(vx*vx)+(vy*vy))-0.25;
if (l<0) l=0;
l=sqrt(l);
vx*=l;
vy*=l;
if (_sweep)
{
sx+=vx;
sy+=vy;
}
else{
sx-=vx;
sy-=vy;
}
a0=atanxy(ax-sx,ay-sy);
a1=atanxy(bx-sx,by-sy);
// ay=divide(ay,e);
// by=divide(by,e);
sy=divide(sy,e);
da=a1-a0;
if (fabs(fabs(da)-pi)<=_acc_zero_ang) // half arc is without larc and sweep is not working instead change a0,a1
{
db=(0.5*(a0+a1))-atanxy(bx-ax,by-ay);
while (db<-pi) db+=pi2; // db<0 CCW ... sweep=1
while (db>+pi) db-=pi2; // db>0 CW ... sweep=0
_sweep=0;
if ((db<0.0)&&(!sweep)) _sweep=1;
if ((db>0.0)&&( sweep)) _sweep=1;
if (_sweep)
{
// a=0; b=0;
if (da>=0.0) a1-=pi2;
if (da< 0.0) a0-=pi2;
}
}
else if (larc) // big arc
{
if ((da< pi)&&(da>=0.0)) a1-=pi2;
if ((da>-pi)&&(da< 0.0)) a0-=pi2;
}
else{ // small arc
if (da>+pi) a1-=pi2;
if (da<-pi) a0-=pi2;
}
da=a1-a0;
// realny stred
c=cos(+ang);
s=sin(+ang);
cx=sx*c-sy*s;
cy=sx*s+sy*c;
}
//---------------------------------------------------------------------------
The atanxy(x,y) is the same as atan2(y,x). You can ignore class svg_usek. Usage of svg_ela is simple first feed the SVG parameters to it:
x0,y0 is start point (from previous <path> element)
x1,y1 is endpoint (x0+dx,y0+dy)
a,b are as yours rx,ry
alfa rotation angle [rad] so you need to convert from degrees...
sweep,larc are as yours.
And then call svg_ela::compute(); that will compute all variables needed for interpolation. When this initialization is done then to obtain any point from the arc just call svg_ela::getpnt(x,y,t); where x,y is the returned coordinate and t=<0,1> is input parameter. All the other methods are not important for you. To render your ARC just do this:
svg_ela arc; // your initialized arc here
int e; double x,y,t;
arc.getpnt(x,y,0.0);
Canvas->MoveTo(x,y);
for (e=1,t=0.0;e;t+=0.02)
{
if (t>=1.0) { t=1.0; e=0; }
arc.getpnt(x,y,t);
Canvas->LineTo(x,y);
}
Do not forget that SVG <g> and <path> can have transform matrices so you should apply them after each svg_ela::getpnt(x,y,t) call.
If you are interested how the stuff works compute() simply:
rotates the space so the ellipse semi-axises are axis aligned.
scale the space so ellipse becomes circle.
compute center point for circle
center lies on line that is perpendicular to line (x0,y0),(x1,y1) and also lies on its midpoint. The distance is computed by Pytagoras and direction from sweep and larc combination.
scale back to ellipse
rotate back
Now we have real center position so also compute the real endpoint angles relative to it. Now for each point on ellipse it is enough to compute it by standard parametric equation of ellipse and rotate to desired position which is what getpnt(x,y,t) does.
Hope it helps a bit.
Here related QA:
Express SVG arc as series of curves
with some images explaining the math behind SVG arcs (using the same variable names as here)
For my Java SVG application I needed a conversion of path arc to lines. I used the above code and converted it into a Java class and performed some cleanup.
package de.berndbock.tinysvg.helper;
/**
* Breaks down SVG arcs into line segments.
*
* #author Bernd Bock <chef#bernd-bock.de>
*/
public class ArcSegmenter {
private static final double PI2 = Math.PI * 2;
private static final double ACC_ZERO_ANG = 0.000001 * Math.PI / 180.0;
private final double x0;
private final double y0;
private final double x1;
private final double y1;
private final double a;
private final double b;
private final double alfa;
private final boolean sweep;
private final boolean larc;
private double sx, sy, a0, a1, da, ang; // sx, sy rotated center by ang
// private double cx, cy; // real center
public ArcSegmenter(double x0, double y0, double x1, double y1 , double a, double b, double alfa, int sweep, int larc) {
this.x0 = x0;
this.y0 = y0;
this.x1 = x1;
this.y1 = y1;
this.a = a;
this.b = b;
this.alfa = alfa;
this.sweep = sweep != 0;
this.larc = larc != 0;
compute();
}
private void compute() {
double ax, ay, bx, by; // body
double vx, vy, l, db;
boolean _sweep;
double c, s, e;
ang = Math.PI - alfa;
_sweep = sweep;
if (larc) {
_sweep = !_sweep;
}
e = a / b;
c = Math.cos(ang);
s = Math.sin(ang);
ax = x0 * c - y0 * s;
ay = x0 * s + y0 * c;
bx = x1 * c - y1 * s;
by = x1 * s + y1 * c;
ay *= e; // transform to circle
by *= e;
sx = 0.5 * (ax + bx); // mid point between A,B
sy = 0.5 * (ay + by);
vx = (ay - by);
vy = (bx - ax);
l = a * a / (vx * vx + vy * vy) - 0.25;
if (l < 0) {
l = 0;
}
l = Math.sqrt(l);
vx *= l;
vy *= l;
if (_sweep) {
sx += vx;
sy += vy;
}
else {
sx -= vx;
sy -= vy;
}
a0 = Math.atan2(ay - sy, ax - sx);
a1 = Math.atan2(by - sy, bx - sx);
sy = sy / e;
da = a1 - a0;
if (Math.abs(Math.abs(da) - Math.PI) <= ACC_ZERO_ANG) { // half arc is without larc and sweep is not working instead change a0,a1
db = (0.5 * (a0 + a1)) - Math.atan2(by - ay, bx - ax);
while (db < -Math.PI) {
db += PI2; // db<0 CCW ... sweep=1
}
while (db > Math.PI) {
db -= PI2; // db>0 CW ... sweep=0
}
_sweep = false;
if ((db < 0.0) && (!sweep)) {
_sweep = true;
}
if ((db > 0.0) && ( sweep)) {
_sweep = true;
}
if (_sweep) {
if (da >= 0.0) {
a1 -= PI2;
}
if (da < 0.0) {
a0 -= PI2;
}
}
}
else if (larc) { // big arc
if ((da < Math.PI) && (da >= 0.0)) {
a1 -= PI2;
}
if ((da > -Math.PI) && (da < 0.0)) {
a0 -= PI2;
}
}
else { // small arc
if (da > Math.PI) {
a1 -= PI2;
}
if (da < -Math.PI) {
a0 -= PI2;
}
}
da = a1 - a0;
// center point calculation:
// c = Math.cos(ang);
// s = Math.sin(ang);
// cx = sx * c - sy * s;
// cy = sx * s + sy * c;
}
public Point getpnt(double t) {
Point result = new Point();
double c, s, x, y;
t = a0 + da * t;
x = sx + a * Math.cos(t);
y = sy + b * Math.sin(t);
c = Math.cos(-ang);
s = Math.sin(-ang);
result.x = x * c - y * s;
result.y = x * s + y * c;
return result;
}
// public Point getCenterPoint() {
// return new Point(cx, cy);
// }
}
If you need the center point, then uncomment the respective lines.
Sample code to give you an idea of the usage:
ArcSegmenter segmenter = new ArcSegmenter(currentPoint.x, currentPoint.y, endPoint.x, endPoint.y, rx, ry, phi, sf, lf);
Point p1, p2;
p1 = segmenter.getpnt(0.0);
Line line;
for (double t = increment; t < 1.000001f; t += increment) {
p2 = segmenter.getpnt(t);
line = new Line(null, parent, p1.x, p1.y, p2.x, p2.y);
elements.add(line);
p1 = p2;
}
I hope there will be an easy answer, as often times, something stripped out of Compact Framework has a way of being performed in a seemingly roundabout manner, but works just as well as the full framework (or can be made more efficient).
Simply put, I wish to be able to do a function similar to System.Drawing.Graphics.DrawArc(...) in Compact Framework 2.0.
It is for a UserControl's OnPaint override, where an arc is being drawn inside an ellipse I already filled.
Essentially (close pseudo code, please ignore imperfections in parameters):
FillEllipse(ellipseFillBrush, largeEllipseRegion);
DrawArc(arcPen, innerEllipseRegion, startAngle, endAngle); //not available in CF
I am only drawing arcs in 90 degree spaces, so the bottom right corner of the ellipse's arc, or the top left. If the answer for ANY angle is really roundabout, difficult, or inefficient, while there's an easy solution for just doing just a corner of an ellipse, I'm fine with the latter, though the former would help anyone else who has a similar question.
I use this code, then use FillPolygon or DrawPolygon with the output points:
private Point[] CreateArc(float StartAngle, float SweepAngle, int PointsInArc, int Radius, int xOffset, int yOffset, int LineWidth)
{
if(PointsInArc < 0)
PointsInArc = 0;
if(PointsInArc > 360)
PointsInArc = 360;
Point[] points = new Point[PointsInArc * 2];
int xo;
int yo;
int xi;
int yi;
float degs;
double rads;
for(int p = 0 ; p < PointsInArc ; p++)
{
degs = StartAngle + ((SweepAngle / PointsInArc) * p);
rads = (degs * (Math.PI / 180));
xo = (int)(Radius * Math.Sin(rads));
yo = (int)(Radius * Math.Cos(rads));
xi = (int)((Radius - LineWidth) * Math.Sin(rads));
yi = (int)((Radius - LineWidth) * Math.Cos(rads));
xo += (Radius + xOffset);
yo = Radius - yo + yOffset;
xi += (Radius + xOffset);
yi = Radius - yi + yOffset;
points[p] = new Point(xo, yo);
points[(PointsInArc * 2) - (p + 1)] = new Point(xi, yi);
}
return points;
}
I had this exactly this problem and me and my team solved that creating a extension method for compact framework graphics class;
I hope I could help someone, cuz I spent a lot of work to get this nice solution
Mauricio de Sousa Coelho
Embedded Software Engineer
public static class GraphicsExtension
{
// Implements the native Graphics.DrawArc as an extension
public static void DrawArc(this Graphics g, Pen pen, float x, float y, float width, float height, float startAngle, float sweepAngle)
{
//Configures the number of degrees for each line in the arc
int degreesForNewLine = 5;
//Calculates the number of points in the arc based on the degrees for new line configuration
int pointsInArc = Convert.ToInt32(Math.Ceiling(sweepAngle / degreesForNewLine)) + 1;
//Minimum points for an arc is 3
pointsInArc = pointsInArc < 3 ? 3 : pointsInArc;
float centerX = (x + width) / 2;
float centerY = (y + height) / 2;
Point previousPoint = GetEllipsePoint(x, y, width, height, startAngle);
//Floating point precision error occurs here
double angleStep = sweepAngle / pointsInArc;
Point nextPoint;
for (int i = 1; i < pointsInArc; i++)
{
//Increments angle and gets the ellipsis associated to the incremented angle
nextPoint = GetEllipsePoint(x, y, width, height, (float)(startAngle + angleStep * i));
//Connects the two points with a straight line
g.DrawLine(pen, previousPoint.X, previousPoint.Y, nextPoint.X, nextPoint.Y);
previousPoint = nextPoint;
}
//Garantees connection with the last point so that acumulated errors cannot
//cause discontinuities on the drawing
nextPoint = GetEllipsePoint(x, y, width, height, startAngle + sweepAngle);
g.DrawLine(pen, previousPoint.X, previousPoint.Y, nextPoint.X, nextPoint.Y);
}
// Retrieves a point of an ellipse with equation:
private static Point GetEllipsePoint(float x, float y, float width, float height, float angle)
{
return new Point(Convert.ToInt32(((Math.Cos(ToRadians(angle)) * width + 2 * x + width) / 2)), Convert.ToInt32(((Math.Sin(ToRadians(angle)) * height + 2 * y + height) / 2)));
}
// Converts an angle in degrees to the same angle in radians.
private static float ToRadians(float angleInDegrees)
{
return (float)(angleInDegrees * Math.PI / 180);
}
}
Following up from #ctacke's response, which created an arc-shaped polygon for a circle (height == width), I edited it further and created a function for creating a Point array for a curved line, as opposed to a polygon, and for any ellipse.
Note: StartAngle here is NOON position, 90 degrees is the 3 o'clock position, so StartAngle=0 and SweepAngle=90 makes an arc from noon to 3 o'clock position.
The original DrawArc method has the 3 o'clock as 0 degrees, and 90 degrees is the 6 o'clock position. Just a note in replacing DrawArc with CreateArc followed by DrawLines with the resulting Point[] array.
I'd play with this further to change that, but why break something that's working?
private Point[] CreateArc(float StartAngle, float SweepAngle, int PointsInArc, int ellipseWidth, int ellipseHeight, int xOffset, int yOffset)
{
if (PointsInArc < 0)
PointsInArc = 0;
if (PointsInArc > 360)
PointsInArc = 360;
Point[] points = new Point[PointsInArc];
int xo;
int yo;
float degs;
double rads;
//could have WidthRadius and HeightRadius be parameters, but easier
// for maintenance to have the diameters sent in instead, matching closer
// to DrawEllipse and similar methods
double radiusW = (double)ellipseWidth / 2.0;
double radiusH = (double)ellipseHeight / 2.0;
for (int p = 0; p < PointsInArc; p++)
{
degs = StartAngle + ((SweepAngle / PointsInArc) * p);
rads = (degs * (Math.PI / 180));
xo = (int)Math.Round(radiusW * Math.Sin(rads), 0);
yo = (int)Math.Round(radiusH * Math.Cos(rads), 0);
xo += (int)Math.Round(radiusW, 0) + xOffset;
yo = (int)Math.Round(radiusH, 0) - yo + yOffset;
points[p] = new Point(xo, yo);
}
return points;
}
What I'm doing is testing to see what the level of intersection between a circle and rectangle. I would like to find whether the rectangle is completely inside the circle, partially intersecting it, or if there is no intersection at all.
I've attached the code that I've come up with today, it simply checks the distances from the center of the circle to the corners of the rectangle to determine the level of intersection.
What I'm wondering is there a more efficient way of doing this?
EDIT:
Here is my updated, working code. fullIntersect is my own, I found the partialIntersect snippet on Circle-Rectangle collision detection (intersection). I'm going to leave this open, as I'm still curious as to whether there is a better way of doing this.
public boolean fullIntersect(float circleX, float circleY, float radius)
{
float radsq = radius * radius;
double xsq = Math.pow(circleX - xPosition, 2);
double xpwsq = Math.pow(circleX - (xPosition + width), 2);
double ysq = Math.pow(circleY - yPosition, 2);
double yphsq = Math.pow(circleY - (yPosition + height), 2);
if(xsq + ysq > radsq || xsq + yphsq > radsq || xpwsq + yphsq > radsq || xpwsq + ysq > radsq)
return false;
return true;
/* this is what the one if statement does
double disBotLeft = xsq + ysq;
double disTopLeft = xsq + yphsq;
double disTopRight = xpwsq + yphsq;
double disBotRight = xpwsq + ysq;
if(disBotRight > radsq) return false;
if(disBotLeft > radsq) return false;
if(disTopLeft > radsq) return false;
if(disTopRight > radsq) return false;
return true;
*/
}
public int intersects(float circleX, float circleY, float radius)
{
if(!enabled) return 0;
double wo2 = width / 2.0d;
double ho2 = height / 2.0d;
double circleDistanceX = Math.abs(circleX - xPosition - wo2);
double circleDistanceY = Math.abs(circleY - yPosition - ho2);
if (circleDistanceX > (wo2 + radius)) { return 0; }
if (circleDistanceY > (ho2 + radius)) { return 0; }
if(fullIntersect(circleX, circleY, radius)) { return 2; }
if (circleDistanceX <= (wo2)) { return 1; }
if (circleDistanceY <= (ho2)) { return 1; }
double cornerDistance_sq = Math.pow(circleDistanceX - wo2,2) +
Math.pow(circleDistanceY - ho2,2);
return cornerDistance_sq <= (radius*radius) ? 1 : 0;
}
I think your code does not consider these intersections:
I'll delete this answer as soon as you enhance your code/question.
I need a good source for reading up on how to create a algorithm to take two polylines (a path comprised of many lines) and performing a union, subtraction, or intersection between them. This is tied to a custom API so I need to understand the underlying algorithm.
Plus any sources in a VB dialect would be doubly helpful.
This catalogue of implementations of intersection algorithms from the Stony Brook Algorithm Repository might be useful. The repository is managed by Steven Skiena,
author of a very well respected book on algorithms: The Algorithm Design Manual.
That's his own Amazon exec link by the way :)
Several routines for you here. Hope you find them useful :-)
// routine to calculate the square of either the shortest distance or largest distance
// from the CPoint to the intersection point of a ray fired at an angle flAngle
// radians at an array of line segments
// this routine returns TRUE if an intersection has been found in which case flD
// is valid and holds the square of the distance.
// and returns FALSE if no valid intersection was found
// If an intersection was found, then intersectionPoint is set to the point found
bool CalcIntersection(const CPoint &cPoint,
const float flAngle,
const int nVertexTotal,
const CPoint *pVertexList,
const BOOL bMin,
float &flD,
CPoint &intersectionPoint)
{
float d, dsx, dsy, dx, dy, lambda, mu, px, py;
int p0x, p0y, p1x, p1y;
// get source position
const float flSx = (float)cPoint.x;
const float flSy = -(float)cPoint.y;
// calc trig functions
const float flTan = tanf(flAngle);
const float flSin = sinf(flAngle);
const float flCos = cosf(flAngle);
const bool bUseSin = fabsf(flSin) > fabsf(flCos);
// initialise distance
flD = (bMin ? FLT_MAX : 0.0f);
// for each line segment in protective feature
for(int i = 0; i < nVertexTotal; i++)
{
// get coordinates of line (negate the y value so the y-axis is upwards)
p0x = pVertexList[i].x;
p0y = -pVertexList[i].y;
p1x = pVertexList[i + 1].x;
p1y = -pVertexList[i + 1].y;
// calc. deltas
dsx = (float)(cPoint.x - p0x);
dsy = (float)(-cPoint.y - p0y);
dx = (float)(p1x - p0x);
dy = (float)(p1y - p0y);
// calc. denominator
d = dy * flTan - dx;
// if line & ray are parallel
if(fabsf(d) < 1.0e-7f)
continue;
// calc. intersection point parameter
lambda = (dsy * flTan - dsx) / d;
// if intersection is not valid
if((lambda <= 0.0f) || (lambda > 1.0f))
continue;
// if sine is bigger than cosine
if(bUseSin){
mu = ((float)p0x + lambda * dx - flSx) / flSin;
} else {
mu = ((float)p0y + lambda * dy - flSy) / flCos;
}
// if intersection is valid
if(mu >= 0.0f){
// calc. intersection point
px = (float)p0x + lambda * dx;
py = (float)p0y + lambda * dy;
// calc. distance between intersection point & source point
dx = px - flSx;
dy = py - flSy;
d = dx * dx + dy * dy;
// compare with relevant value
if(bMin){
if(d < flD)
{
flD = d;
intersectionPoint.x = RoundValue(px);
intersectionPoint.y = -RoundValue(py);
}
} else {
if(d > flD)
{
flD = d;
intersectionPoint.x = RoundValue(px);
intersectionPoint.y = -RoundValue(py);
}
}
}
}
// return
return(bMin ? (flD != FLT_MAX) : (flD != 0.0f));
}
// Routine to calculate the square of the distance from the CPoint to the
// intersection point of a ray fired at an angle flAngle radians at a line.
// This routine returns TRUE if an intersection has been found in which case flD
// is valid and holds the square of the distance.
// Returns FALSE if no valid intersection was found.
// If an intersection was found, then intersectionPoint is set to the point found.
bool CalcIntersection(const CPoint &cPoint,
const float flAngle,
const CPoint &PointA,
const CPoint &PointB,
const bool bExtendLine,
float &flD,
CPoint &intersectionPoint)
{
// get source position
const float flSx = (float)cPoint.x;
const float flSy = -(float)cPoint.y;
// calc trig functions
float flTan = tanf(flAngle);
float flSin = sinf(flAngle);
float flCos = cosf(flAngle);
const bool bUseSin = fabsf(flSin) > fabsf(flCos);
// get coordinates of line (negate the y value so the y-axis is upwards)
const int p0x = PointA.x;
const int p0y = -PointA.y;
const int p1x = PointB.x;
const int p1y = -PointB.y;
// calc. deltas
const float dsx = (float)(cPoint.x - p0x);
const float dsy = (float)(-cPoint.y - p0y);
float dx = (float)(p1x - p0x);
float dy = (float)(p1y - p0y);
// Calc. denominator
const float d = dy * flTan - dx;
// If line & ray are parallel
if(fabsf(d) < 1.0e-7f)
return false;
// calc. intersection point parameter
const float lambda = (dsy * flTan - dsx) / d;
// If extending line to meet point, don't check for ray missing line
if(!bExtendLine)
{
// If intersection is not valid
if((lambda <= 0.0f) || (lambda > 1.0f))
return false; // Ray missed line
}
// If sine is bigger than cosine
float mu;
if(bUseSin){
mu = ((float)p0x + lambda * dx - flSx) / flSin;
} else {
mu = ((float)p0y + lambda * dy - flSy) / flCos;
}
// if intersection is valid
if(mu >= 0.0f)
{
// calc. intersection point
const float px = (float)p0x + lambda * dx;
const float py = (float)p0y + lambda * dy;
// calc. distance between intersection point & source point
dx = px - flSx;
dy = py - flSy;
flD = (dx * dx) + (dy * dy);
intersectionPoint.x = RoundValue(px);
intersectionPoint.y = -RoundValue(py);
return true;
}
return false;
}
// Fillet (with a radius of 0) two lines. From point source fired at angle (radians) to line Line1A, Line1B.
// Modifies line end point Line1B. If the ray does not intersect line, then it is rotates every 90 degrees
// and tried again until fillet is complete.
void Fillet(const CPoint &source, const float fThetaRadians, const CPoint &Line1A, CPoint &Line1B)
{
if(Line1A == Line1B)
return; // No line
float dist;
if(CalcIntersection(source, fThetaRadians, Line1A, Line1B, true, dist, Line1B))
return;
if(CalcIntersection(source, CalcBaseFloat(TWO_PI, fThetaRadians + PI * 0.5f), Line1A, Line1B, true, dist, Line1B))
return;
if(CalcIntersection(source, CalcBaseFloat(TWO_PI, fThetaRadians + PI), Line1A, Line1B, true, dist, Line1B))
return;
if(!CalcIntersection(source, CalcBaseFloat(TWO_PI, fThetaRadians + PI * 1.5f), Line1A, Line1B, true, dist, Line1B))
ASSERT(FALSE); // Could not find intersection?
}
// routine to determine if an array of line segments cross gridSquare
// x and y give the float coordinates of the corners
BOOL CrossGridSquare(int nV, const CPoint *pV,
const CRect &extent, const CRect &gridSquare)
{
// test extents
if( (extent.right < gridSquare.left) ||
(extent.left > gridSquare.right) ||
(extent.top > gridSquare.bottom) ||
(extent.bottom < gridSquare.top))
{
return FALSE;
}
float a, b, c, dx, dy, s, x[4], y[4];
int max_x, max_y, min_x, min_y, p0x, p0y, p1x, p1y, sign, sign_old;
// construct array of vertices for grid square
x[0] = (float)gridSquare.left;
y[0] = (float)gridSquare.top;
x[1] = (float)(gridSquare.right);
y[1] = y[0];
x[2] = x[1];
y[2] = (float)(gridSquare.bottom);
x[3] = x[0];
y[3] = y[2];
// for each line segment
for(int i = 0; i < nV; i++)
{
// get end-points
p0x = pV[i].x;
p0y = pV[i].y;
p1x = pV[i + 1].x;
p1y = pV[i + 1].y;
// determine line extent
if(p0x > p1x){
min_x = p1x;
max_x = p0x;
} else {
min_x = p0x;
max_x = p1x;
}
if(p0y > p1y){
min_y = p1y;
max_y = p0y;
} else {
min_y = p0y;
max_y = p1y;
}
// test to see if grid square is outside of line segment extent
if( (max_x < gridSquare.left) ||
(min_x > gridSquare.right) ||
(max_y < gridSquare.top) ||
(min_y > gridSquare.bottom))
{
continue;
}
// calc. line equation
dx = (float)(p1x - p0x);
dy = (float)(p1y - p0y);
a = dy;
b = -dx;
c = -dy * (float)p0x + dx * (float)p0y;
// evaluate line eqn. at first grid square vertex
s = a * x[0] + b * y[0] + c;
if(s < 0.0f){
sign_old = -1;
} else if(s > 1.0f){
sign_old = 1;
} else {
sign_old = 0;
}
// evaluate line eqn. at other grid square vertices
for (int j = 1; j < 4; j++)
{
s = a * x[j] + b * y[j] + c;
if(s < 0.0f){
sign = -1;
} else if(s > 1.0f){
sign = 1;
} else {
sign = 0;
}
// if there has been a chnage in sign
if(sign != sign_old)
return TRUE;
}
}
return FALSE;
}
// calculate the square of the shortest distance from point s
// and the line segment between p0 and p1
// t is the point on the line from which the minimum distance
// is measured
float CalcShortestDistanceSqr(const CPoint &s,
const CPoint &p0,
const CPoint &p1,
CPoint &t)
{
// if point is at a vertex
if((s == p0) || (s == p1))
return(0.0F);
// calc. deltas
int dx = p1.x - p0.x;
int dy = p1.y - p0.y;
int dsx = s.x - p0.x;
int dsy = s.y - p0.y;
// if both deltas are zero
if((dx == 0) && (dy == 0))
{
// shortest distance is distance is to either vertex
float l = (float)(dsx * dsx + dsy * dsy);
t = p0;
return(l);
}
// calc. point, p, on line that is closest to sourcePosition
// p = p0 + l * (p1 - p0)
float l = (float)(dsx * dx + dsy * dy) / (float)(dx * dx + dy * dy);
// if intersection is beyond p0
if(l <= 0.0F){
// shortest distance is to p0
l = (float)(dsx * dsx + dsy * dsy);
t = p0;
// else if intersection is beyond p1
} else if(l >= 1.0F){
// shortest distance is to p1
dsx = s.x - p1.x;
dsy = s.y - p1.y;
l = (float)(dsx * dsx + dsy * dsy);
t = p1;
// if intersection is between line end points
} else {
// calc. perpendicular distance
float ldx = (float)dsx - l * (float)dx;
float ldy = (float)dsy - l * (float)dy;
t.x = p0.x + RoundValue(l * (float)dx);
t.y = p0.y + RoundValue(l * (float)dy);
l = ldx * ldx + ldy * ldy;
}
return(l);
}
// Calculates the bounding rectangle around a set of points
// Returns TRUE if the rectangle is not empty (has area), FALSE otherwise
// Opposite of CreateRectPoints()
BOOL CalcBoundingRectangle(const CPoint *pVertexList, const int nVertexTotal, CRect &rect)
{
rect.SetRectEmpty();
if(nVertexTotal < 2)
{
ASSERT(FALSE); // Must have at least 2 points
return FALSE;
}
// First point, set rectangle (no area at this point)
rect.left = rect.right = pVertexList[0].x;
rect.top = rect.bottom = pVertexList[0].y;
// Increst rectangle by looking at other points
for(int n = 1; n < nVertexTotal; n++)
{
if(rect.left > pVertexList[n].x) // Take minimum
rect.left = pVertexList[n].x;
if(rect.right < pVertexList[n].x) // Take maximum
rect.right = pVertexList[n].x;
if(rect.top > pVertexList[n].y) // Take minimum
rect.top = pVertexList[n].y;
if(rect.bottom < pVertexList[n].y) // Take maximum
rect.bottom = pVertexList[n].y;
}
rect.NormalizeRect(); // Normalise rectangle
return !(rect.IsRectEmpty());
}