Physics 5 
In class we developed code which I’ve since modified a bit. Here’s the header file:
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// G. Hagopian Triangle.h #include <ctime>
class Triangle { public : Triangle() { _vrt[0][0] = 320; _vrt[0][1] = 240; _vrt[1][0] = 330; _vrt[1][1] = 240; _vrt[2][0] = 320; _vrt[2][1] = 230; findCentroid(); } Triangle(double
x0, double y0, _vrt[0][0] = x0; _vrt[0][1] = y0; _vrt[1][0] = x1; _vrt[1][1] = y1; _vrt[2][0] = x2; _vrt[2][1] = y2; findCentroid(); } //~Triangle(); void findSides(); // use distance formula for triangle sides void findAngles(); // use law of cosines for interior angles void findArea(); void findSlopes(); // slopes of the sides void findBisectors(); // angle bisectors void findIncenter(); // intrsctn angle bisctrs (also incircle cntr) void findCentroid(); // compute _centroid[3] - the coords of centroid void findHeights(); // altitudes void findInradius(); // radius of inscribed circle void findOrthocenter(); // intersection of altitudes void findCircumCircle(); // intersection of perpendicular bisectors void find9PtCircleCenter(); // center of nine point circle // drawing void draw(); // draw triangle void drawIncircle() {dbCircle(_incenter[0],_incenter[1],_inradius);} void drawMedians(); // a median connects a vertex to midpt of opp void drawAngleBisectors(); // these intersect at incenter void drawPerpBisectors(); // these intersect at circumcenter void drawCircumcircle(); // void drawEulerLine(); // line thru orthocntr, circumcntr & cntrd void drawNinePointCircle(); // cntr // rotations void rotateAboutZero(double); // zero is upper left corner void rotateAboutCentroid(double); // circle rotates in place void rotateAboutPoint(double, double pt[]); // rotate any point
private : double _vrt[3][2]; // coords of vertices double _sides[3]; // dist formula computes side lengths double _angles[3]; // law of cosines for angles double _area; // triangle's area double _slopes[3]; // slope of each side or 1.e8 for vertical double _heights[3]; // simple right triangle trig for altitudes double _feet[3][2]; // ??? double _midpoints[3][2]; // ??? double _incenter[2]; // weighted average of three sides double _inradius; // 1/(1/_heights[0]+1/_heights[1]+1/_heights[2]) double _circumCenter[2]; // center of circumcircle double _circumRadius; // radius of circumcircle double _centroid[2]; // intersection of medians double _orthocenter[2]; // intersection of perpendicular bisectors double ninePtCircleCenter[2]; // };
void Triangle::draw() { dbLine(_vrt[1][0],_vrt[1][1],_vrt[2][0],_vrt[2][1]); dbLine(_vrt[0][0],_vrt[0][1],_vrt[2][0],_vrt[2][1]); dbLine(_vrt[0][0],_vrt[0][1],_vrt[1][0],_vrt[1][1]); }
void Triangle::rotateAboutZero(double
theta) { _vrt[0][0] = (_vrt[0][0]*dbCOS(theta)-_vrt[0][1]*dbSIN(theta)); _vrt[0][1] = (_vrt[0][0]*dbSIN(theta)+_vrt[0][1]*dbCOS(theta)); _vrt[1][0] = (_vrt[1][0]*dbCOS(theta)-_vrt[1][1]*dbSIN(theta)); _vrt[1][1] = (_vrt[1][0]*dbSIN(theta)+_vrt[1][1]*dbCOS(theta)); _vrt[2][0] = (_vrt[2][0]*dbCOS(theta)-_vrt[2][1]*dbSIN(theta)); _vrt[2][1] = (_vrt[2][0]*dbSIN(theta)+_vrt[2][1]*dbCOS(theta)); }
void Triangle::findCentroid() { // averages _centroid[0] = (_vrt[0][0]+_vrt[1][0]+_vrt[2][0])/3.; _centroid[1] = (_vrt[0][1]+_vrt[1][1]+_vrt[2][1])/3.; }
void Triangle::rotateAboutCentroid(double theta) { // dbCOS vs cos? _vrt[0][0] = (_centroid[0] + (_vrt[0][0]-_centroid[0])*dbCOS(theta)- (_vrt[0][1]-_centroid[1])*dbSIN(theta)); _vrt[0][1] = (_centroid[1] + (_vrt[0][0]-_centroid[0])*dbSIN(theta)+ (_vrt[0][1]-_centroid[1])*dbCOS(theta)); _vrt[1][0] = (_centroid[0] + (_vrt[1][0]-_centroid[0])*dbCOS(theta)- (_vrt[1][1]-_centroid[1])*dbSIN(theta)); _vrt[1][1] = (_centroid[1] + (_vrt[1][0]-_centroid[0])*dbSIN(theta)+ (_vrt[1][1]-_centroid[1])*dbCOS(theta)); _vrt[2][0] = (_centroid[0] + (_vrt[2][0]-_centroid[0])*dbCOS(theta)- (_vrt[2][1]-_centroid[1])*dbSIN(theta)); _vrt[2][1] = (_centroid[1] + (_vrt[2][0]-_centroid[0])*dbSIN(theta)+ (_vrt[2][1]-_centroid[1])*dbCOS(theta)); }
void Triangle::findArea() { // need code for this still }
void Triangle::findSlopes() { if(_vrt[1][0] != _vrt[2][0]) _slopes[0] = (_vrt[1][1] - _vrt[2][1])/(_vrt[1][0] - _vrt[2][0]); else _slopes[0] = 1.e8; // arbitrary very large, finite quantity if(_vrt[0][0] != _vrt[2][0]) _slopes[1] = (_vrt[0][1] - _vrt[2][1])/(_vrt[0][0] - _vrt[2][0]); else _slopes[1] = 1.e8; if(_vrt[0][0] != _vrt[1][0]) _slopes[2] = (_vrt[0][1] - _vrt[1][1])/(_vrt[0][0] - _vrt[1][0]); else _slopes[2] = 1.e8; }
void Triangle::findSides() { _sides[0] = sqrt((_vrt[2][0]-_vrt[1][0])*(_vrt[2][0]-_vrt[1][0])+ (_vrt[2][1]-_vrt[1][1])*(_vrt[2][1]-_vrt[1][1])); _sides[1] = sqrt((_vrt[2][0]-_vrt[0][0])*(_vrt[2][0]-_vrt[0][0])+ (_vrt[2][1]-_vrt[0][1])*(_vrt[2][1]-_vrt[0][1])); _sides[2] = sqrt((_vrt[1][0]-_vrt[0][0])*(_vrt[1][0]-_vrt[0][0])+ (_vrt[1][1]-_vrt[0][1])*(_vrt[1][1]-_vrt[0][1])); }
void Triangle::findIncenter() { double perimeter = _sides[0]+_sides[1]+_sides[2]; _incenter[0] = (_sides[0]*_vrt[0][0] +_sides[1]*_vrt[1][0] +_sides[2]*_vrt[2][0])/perimeter; _incenter[1] = (_sides[0]*_vrt[0][1] +_sides[1]*_vrt[1][1] +_sides[2]*_vrt[2][1])/perimeter; }
void Triangle::findAngles() { // maybe change to use law of sines for 2nd? _angles[0] = dbACOS((_sides[1]*_sides[1]+ _angles[1] =
dbACOS((_sides[0]*_sides[0]+ _angles[2] = dbACOS((_sides[1]*_sides[1]+ _sides[0]*_sides[0]- _sides[2]*_sides[2])/(2*_sides[1]*_sides[0])); }
void Triangle::findHeights() { _heights[0]=_sides[2]*dbSIN(_angles[1]); _heights[1]=_sides[0]*dbSIN(_angles[2]); _heights[2]=_sides[1]*dbSIN(_angles[0]); }
void Triangle::findInradius() { _inradius = 1/(1/_heights[0]+1/_heights[1]+1/_heights[2]); }
void Triangle::findCircumCircle() { // need code for this still }
void Triangle::drawCircumcircle() { // need code for this still } |
And the DarkGDK() (or main()) function code is below:
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// G. Hagopian - trnglMain.cpp #include "DarkGDK.h" #include "Triangle03.h" #include <ctime>
void updateTriangle(Triangle *); const DWORD BLACK = dbRGB(0,0,0); const DWORD WHITE = dbRGB(255,255,255);
void DarkGDK() { srand((unsigned int)time(NULL)); // seed random number generator Triangle T0; // create triangle with default constructor Triangle T1(100,100,200,200,150,250);// triangle with specified vertices //Create a dynamic array with 81 triangles Triangle * trngls[81]; Triangle * tPtr; for (int i = 0; i < 9; i++) { for(int j = 0; j < 9; j++) { tPtr = new
Triangle((double)(64*(i+1)+(rand()%50)), (double)(64*(i+1)+(rand()%50)), (double)(64*(i+1)+(rand()%50)), // note use of place value here for array indexing trngls[9*i+j] = tPtr; } } dbSyncOn(); dbSyncRate(60); while( LoopGDK() ) { T0.draw(); T0.rotateAboutZero(1); T1.draw(); T1.drawIncircle(); T1.rotateAboutCentroid(1); for(int i = 0; i < 81; ++i) { updateTriangle(trngls[i]); } dbSync(); dbCLS(WHITE); } // end game loop. for (int i = 0; i < 81; i++) { delete trngls[i]; trngls[i] = NULL; } // end for } // end DarkGDK().
void updateTriangle(Triangle * T) { // passing pointer like passing reference dbInk(dbRGB(50+rand()%200,50+rand()%200,50+rand()%200),WHITE); T->draw(); T->drawIncircle(); T->rotateAboutCentroid(1); T->findSides(); T->findAngles(); T->findHeights(); T->findIncenter(); T->findInradius(); T->findCircumCircle(); // need code for this still T->drawCircumcircle(); // need code for this still } |
Your job here is to add code for the following:
1.
findCircumCircle(); You can find formulas for the center and
radius of the circumcircle at various internet sites including http://en.wikipedia.org/wiki/Circumscribed_circle
Implement the code by showing how the array of random triangles, their
incircles and circumcircles rotate to produce pictures like these:
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2.
Provide code to define the following functions and use them
also i
void drawMedians(); // a median connects a
vertex to midpt of opp
void drawAngleBisectors(); //
these intersect at incenter
void drawPerpBisectors(); // these intersect at circumcenter
void drawCircumcircle(); //
void drawEulerLine(); // line thru orthocntr, circumcntr & cntrd
void drawNinePointCircle(); // google it
3. Modify the code to allow the user to enter the number of rows and columns of triangles to display and then rotate. In the code it is an evenly spaced 9 by 9 array with random coordinates varying by as much as 50.
4. Try something I wouldn’t have guessed you would invent.