Refactored code, integrated base code (DCEL)

Makefile

@@ -16,14 +16,14 @@
 #	gcc -Wall -Wextra -Werror -pedantic -g -o main.o main.c -c
 
 # Link command:
-voronoi2: common.o geometry.o dcel.o voronoi.o input.o main.o
-	gcc -Wall -Wextra -Werror -pedantic -g -o voronoi2 main.o input.o voronoi.o dcel.o geometry.o common.o
+voronoi2: common.o towers.o dcel.o voronoi.o input.o main.o
+	gcc -Wall -Wextra -Werror -pedantic -g -o voronoi2 main.o input.o voronoi.o dcel.o towers.o common.o -lm
 
 common.o: common.c
 	gcc -Wall -Wextra -Werror -pedantic -g -o common.o common.c -c
 
-geometry.o: geometry.c
-	gcc -Wall -Wextra -Werror -pedantic -g -o geometry.o geometry.c -c
+towers.o: towers.c
+	gcc -Wall -Wextra -Werror -pedantic -g -o towers.o towers.c -c
 
 dcel.o: dcel.c
 	gcc -Wall -Wextra -Werror -pedantic -g -o dcel.o dcel.c -c

common.h

@@ -19,6 +19,13 @@
 
 #endif
 
+#ifndef MATH_HEADER
+#define MATH_HEADER
+
+#include <math.h>
+
+#endif
+
 #ifndef COMMON_HEADER
 #define COMMON_HEADER
 

dcel.h

@@ -1,32 +1,261 @@
-#ifndef GEOMETRY_HEADER
-#include "geometry.h"
-#endif
-
-#ifndef STDIO_HEADER
-#include <stdio.h>
+#ifndef TOWERS_HEADER
+#include "towers.h"
 #endif
 
 #ifndef DCEL_HEADER
 #define DCEL_HEADER
 
-typedef struct halfEdge {
-    struct halfEdge *previous;
-    struct halfEdge *next;
-    struct halfEdge *twin;
+/* Here is the Base Code from Grady, with some alterations by me */
+
+enum intersectType {
+    DOESNT_INTERSECT  = 0, // Doesn't intersect
+    INTERSECT         = 1, // Intersects
+    SAME_LINE_OVERLAP = 2, // Lines are the same
+    ENDS_OVERLAP      = 3  // Intersects at exactly one point (endpoint)
+};
+
+typedef struct vertex {
+    double x;
+    double y;
+} vertex_t;
+
+typedef struct bisector {
+    double startX;
+    double startY;
+    double endX;
+    double endY;
+
+    /* This refers to the midpoint of the line segment AB, not the midpoint
+     * of the bisector itself.
+     */
+    double midX;
+    double midY;
+
+    int isSlopeInfinite;
+    double slope;
+} bisector_t;
+
+typedef struct halfEdgeLabel {
+    struct halfEdgeLabel *previous;
+    struct halfEdgeLabel *next;
+    struct halfEdgeLabel *twin;
     int face;
     int edge;
+    int startVertex;
+    int endVertex;
 } halfEdge_t;
 
 typedef struct edge {
-    halfEdge_t halfEdge;
+    halfEdge_t *halfEdge;
 } edge_t;
 
 typedef struct face {
-    halfEdge_t start;
+    halfEdge_t *start;
+    tower_t *tower;
 } face_t;
 
+typedef struct split {
+    int startEdge;
+    int endEdge;
+    int verticesSpecified;
+    vertex_t startPoint;
+    vertex_t endPoint;
+} split_t;
+
+typedef struct intersection {
+    vertex_t intersectionPoint;
+} intersection_t;
+
+typedef struct DCEL {
+    edge_t *edges;
+    int edgesUsed;
+    int edgesAllocated;
+
+    face_t *faces;
+    int facesUsed;
+    int facesAllocated;
+
+    vertex_t *vertices;
+    int verticesUsed;
+    int verticesAllocated;
+} DCEL_t;
+
+/* Allocate a new DCEL and return it. */
+DCEL_t *newDCEL();
+
+/* Allocate a new halfEdge and return it. */
+halfEdge_t *newHalfEdge();
+
+/* Returns INSIDE if the points is on the INSIDE of the vector twin by the CW 
+ * winding order, OUTSIDE if it is OUTSIDE by the CW winding order, and 
+ * DIR_UNDECIDED if the point lies on the vector between the points v1 and v2. 
+ */
+int getRelativeDir(double x, double y, vertex_t *v1, vertex_t *v2);
+
+/* Takes an established direction and a new direction, and returns 1 if the 
+ * direction matches the decidedDirection or if the direction is undecided.
+ */
+int directionOrUndecided(int decidedDirection, int direction);
+
+/* Check there's space for another vertex in the DCEL, 
+ * or increase the allocated space. 
+ */
+void ensureSpaceForVertex(DCEL_t *dcel);
+
+/* Check there's space for another edge in the DCEL, 
+ * or increase the allocated space. 
+ */
+void ensureSpaceForEdge(DCEL_t *dcel);
+
+/* Check there's space for another face in the DCEL, 
+ * or increase the allocated space. 
+ */
+void ensureSpaceForFace(DCEL_t *dcel);
+
+/* Add an edge from the startVertex index vertex to the endVertex index. 
+ * Only fills one half-edge as other half-edges will always be added 
+ * through geometry construction.
+ */
+void addEdge(DCEL_t *dcel, int startVertex, int endVertex);
+
+/* Add a face to the DCEL given using the given halfEdge and sets the face. */
+void addFace(DCEL_t *dcel, halfEdge_t *he);
+
+/* Reads the polygon from the given file. */
+DCEL_t *readPolygonFile(char *polygonfileName);
+
+/* Reads the next split from the given file. */
+split_t *readNextSplit(FILE *splitfile);
+
+/* Frees a given split.  */
+void freeSplit(split_t *split);
+
+/* Returns 1 if vertices are sufficiently close, 0 otherwise. */
+int vertexMatch(vertex_t *v1, vertex_t *v2);
+
+/* Gets the string for the given bisector equation. */
+char *getBisectorEquation(bisector_t *b);
+
+/* Frees the given bisector. */
+void freeBisector(bisector_t *bisector);
+
+/* Representation of no face */
+#define NOFACE (-1)
+
+/* Default face for intersections. */
+#define DEFAULT_FACE 0
+
+/* Default minimum length for bisector in each direction */
+#define DEFAULTMINLENGTH (200)
+
+/* Gets the intersection between the given bisector and the given DCEL
+ * for the given face. 
+ */
+intersection_t *getIntersection(bisector_t *b, DCEL_t *dcel, \
+    int face, double minLength);
+
+/* Gets the string for the given intersection. */
+char *getIntersectionString(intersection_t *intersection);
+
+/* Frees a given intersection. */
+void freeIntersection(intersection_t *intersection);
+
+/* Applies a given split to the DCEL. */
+void applySplit(split_t *split, DCEL_t *dcel);
+
+/* Frees the given DCEL */
+void freeDCEL(DCEL_t *dcel);
+
+/* Gets the number of faces in the DCEL. */
+int getFaceCount(DCEL_t *dcel);
+
+/* Returns 1 if the given x,y point is inside the given face. */
+int inFace(DCEL_t *dcel, double x, double y, int faceIndex);
+
+/* Gets the diameter of the given face. */
+double getDiameter(DCEL_t *dcel, int faceIndex);
+
+/* Adds the watchtower to the Voronoi diagram represented by the given DCEL, 
+ * applying required splits and setting the watchtower as required.
+ */
+void incrementalVoronoi(DCEL_t *dcel, tower_t *watchTower);
+
+/* Returns the number of vertices in the DCEL. */
+int getDCELPointCount(DCEL_t *dcel);
+
+/* Get x value of given vertex in DCEL. */
+double getDCELVertexX(DCEL_t *dcel, int vertex);
+
+/* Get y value of given vertex in DCEL. */
+double getDCELVertexY(DCEL_t *dcel, int vertex);
+
+/* Returns the number of edges in the DCEL. */
+int getDCELEdgeCount(DCEL_t *dcel);
+
+/* Get start vertex of given edge in DCEL. */
+int getDCELEdgeVertexStart(DCEL_t *dcel, int edge);
+
+/* Get end vertex of given edge in DCEL. */
+int getDCELEdgeVertexEnd(DCEL_t *dcel, int edge);
+
+/* Get start vertex of paired given edge in DCEL. */
+int getDCELEdgeVertexPairStart(DCEL_t *dcel, int edge);
+
+/* Get end vertex of paired given edge in DCEL. */
+int getDCELEdgeVertexPairEnd(DCEL_t *dcel, int edge);
+
+/* Check if the DCEL has the given edge. */
+int DCELhasEdge(DCEL_t *dcel, int edge);
+
+/* Check if the DCEL has a pair for the given edge. */
+int DCELhasEdgePair(DCEL_t *dcel, int edge);
+
+/* My own functions */
+
+/* Reads the polygon file and stores the information in the vertices array */
 vertex_t **readPolygon(vertex_t **vertices, FILE *polygonFile, \
     int *numVertices);
+
+/* Frees an array of vertices */
 void freeVertices(vertex_t **vertices, int numVertices);
 
+/* Calculates and returns the equation of a bisector of two points */
+bisector_t *getBisector(vertex_t *pointA, vertex_t *pointB);
+
+/* Euclidian distance between two 2D points */
+double dist_2D(double x1, double y1, double x2, double y2);
+
+/* Returns a value for x that ensures the point (x, y) is at least d (distance) 
+ * away from (x1, y1) whilst ensuring (x, y) is on the line y = mx + c1.
+ */
+double inv_dist_2D(double x1, double y1, double m, double c, double d);
+
+/* Returns a point at least distance away from the midpoint of the bisector given */
+vertex_t *getBisectorPoint(double distance, bisector_t *b);
+
+/* O'Rourke's functions */
+/* Returns -1, 0 or 1, based on the area enclosed by the three points. 0 corresponds
+    to no area enclosed.
+*/
+int areaSign(double sx, double sy, double ex, double ey, double x, double y);
+
+/* Returns 1 if point (x, y) is between (sx, sy) and (ex, ey) */
+int between(double sx, double sy, double ex, double ey, double x, double y);
+
+/* Returns 1 if the point (x, y) is in the line from s(x, y) to e(x, y),
+ * 0 otherwise.
+ */
+int collinear(double sx, double sy, double ex, double ey, double x, double y);
+
+/* Tests if the half edge and bisector are parallel and overlapping, or not
+ * intersecting.
+ */
+enum intersectType parallelIntersects(double heSx, double heSy, \
+    double heEx, double heEy, double bSx, double bSy, \
+    double bEx, double bEy, double *x, double *y);
+
+/* Tests if  */
+enum intersectType intersects(halfEdge_t *he, bisector_t *b, \
+    DCEL_t *dcel, double minLength, double *x, double *y);
+
 #endif

geometry.c

@@ -1,56 +0,0 @@
-/* geometry.c
- *
- * Created by Rory Healy (healyr@student.unimelb.edu.au)
- * Created on 9th September 2021
- * Last modified 9th September 2021
- *
- * A small library of functions used in the geometric construction of a 
- * Voronoi diagram.
- *
- */
-
-#ifndef GEOMETRY_HEADER
-#include "geometry.h"
-#endif
-
-#ifndef COMMON_HEADER
-#include "common.h"
-#endif
-
-bisector_t getBisector(vertex_t *pointA, vertex_t *pointB) {
-    bisector_t newBisector;
-    double midpointX = (pointA->x + pointB->x) / 2;
-    double midpointY = (pointA->y + pointB->y) / 2;
-
-    newBisector.x = midpointX;
-    newBisector.y = midpointY;
-
-    /* Calculating bisector slope according to slope of AB */
-    if (pointA->x == pointB->x) {
-        /* The line segment AB has an infinite gradient, 
-         * so the orthogonal line will have zero slope.
-         */
-        newBisector.slope = 0;
-        newBisector.isSlopeInfinite = 0;
-    } else if (pointA->y == pointB->y) {
-        /* The line segment AB has gradient of zero, so 
-         * the orthogonal line will have an infinite slope. 
-         */
-        newBisector.isSlopeInfinite = 1;
-
-        /* Not actually zero, just a placeholder to prevent 
-         * accidental errors 
-         */
-        newBisector.slope = 0;
-    } else {
-        /* Slope of the line segment AB */
-        double segmentSlope = \
-            (pointB->y - pointA->y) / (pointB->x - pointA->x);
-
-        /* Calculate orthogonal slope */
-        newBisector.isSlopeInfinite = 0;
-        newBisector.slope = -1 / segmentSlope;
-    }
-
-    return newBisector;
-}

geometry.h

@@ -1,19 +0,0 @@
-#ifndef GEOMETRY_HEADER
-#define GEOMETRY_HEADER
-
-typedef struct vertex {
-    double x;
-    double y;
-} vertex_t;
-
-typedef struct bisector {
-    int isSlopeInfinite;    
-    double slope;
-    double x;
-    double y;
-} bisector_t;
-
-/* Calculates and returns the equation of a bisector of two points */
-bisector_t getBisector(vertex_t *vertexA, vertex_t *vertexB); 
-
-#endif

output.txt

@@ -1,6 +0,0 @@
-y = 0.000000 * (x - 145.600000) + -34.700000
-y = 0.000000 * (x - 145.600000) + -35.200000
-x = 147.100000
-x = 147.100000
-x = 147.600000
-y = 1.000000 * (x - 147.600000) + -33.200000

towers.c

@@ -0,0 +1,97 @@
+
+
+#ifndef TOWERS_HEADER
+#include "towers.h"
+#endif
+
+#define BASE_10 10
+#define MAX_CSV_ENTRY_LEN 512
+#define MAX_FIELD_LEN 128
+#define NUM_CSV_FIELDS 6
+
+tower_t **readTowers(tower_t **towers, FILE *datasetFile, int *numTowers) {
+    /* Maximum length of a single CSV line */
+    size_t lineBufferSize = MAX_CSV_ENTRY_LEN + 1;
+
+    /* Stores the current line from the CSV */
+    char *lineBuffer = malloc(lineBufferSize * sizeof(*lineBuffer));
+    checkNullPointer(lineBuffer);
+
+    int maxSizetowers = 1;
+
+    /* Discard the header line, then read the rest of the CSV */
+    getline(&lineBuffer, &lineBufferSize, datasetFile);
+    while (getline(&lineBuffer, &lineBufferSize, datasetFile) > 0) {
+        /* Check if there enough space in the towers array */
+        if (*numTowers == maxSizetowers) {
+            maxSizetowers *= 2;
+            tower_t **temp = realloc(towers, maxSizetowers * sizeof(*towers));
+            checkNullPointer(temp);
+            towers = temp;
+        }
+
+        /* The current tower being filled in with information */
+        towers[*numTowers] = malloc(sizeof(*towers[*numTowers]));
+
+        readCurrentTower(lineBuffer, towers[*numTowers]);
+        *numTowers += 1;    
+    }
+    free(lineBuffer);
+    return towers;
+}
+
+void readCurrentTower(char *lineBuffer, tower_t *tower) {
+    /* Stores the current CSV field for the current line */
+    char *token = strtok(lineBuffer, ",");
+    size_t tokenLength;
+
+    for (int i = 0; i < NUM_CSV_FIELDS; i++) {
+        tokenLength = strlen(token);
+        switch(i) {
+            /* Case 0, 1, and 3 deal with strings
+             * Case 2 deals with an integer
+             * Case 4 and 5 deal with doubles
+             * Each case is handled seperately to fill in the
+             * tower with no space wasted.
+             */
+            case 0:
+                tower->id = malloc(sizeof(char) * tokenLength + 1);
+                checkNullPointer(tower->id);
+                strcpy(tower->id, token);
+                tower->id[tokenLength] = '\0';
+                break;
+            case 1:
+                tower->postcode = malloc(sizeof(char) * tokenLength + 1);
+                checkNullPointer(tower->postcode);
+                strcpy(tower->postcode, token);
+                tower->postcode[tokenLength] = '\0';
+                break;
+            case 2:
+                tower->population = strtol(token, NULL, BASE_10);
+                break;
+            case 3:
+                tower->manager = malloc(sizeof(char) * tokenLength + 1);
+                checkNullPointer(tower->manager);
+                strcpy(tower->manager, token);
+                tower->manager[tokenLength] = '\0';
+                break;
+            case 4:
+                tower->x = strtod(token, NULL);
+                break;
+            case 5:
+                tower->y = strtod(token, NULL);
+                break;
+        }
+        token = strtok(NULL, ",");
+    }
+}
+
+void freeTowers(tower_t **towers, int numTowers) {
+    for (int i = 0; i < numTowers; i++) {
+        free(towers[i]->id);
+        free(towers[i]->manager);
+        free(towers[i]->postcode);
+        free(towers[i]);
+    }
+    free(towers);
+}

towers.h

@@ -0,0 +1,26 @@
+#ifndef COMMON_HEADER
+#include "common.h"
+#endif
+
+#ifndef TOWERS_HEADER
+#define TOWERS_HEADER
+
+typedef struct tower {
+    char *id;
+    char *postcode;
+    char *manager;
+    int population;
+    double x;
+    double y;
+} tower_t;
+
+/* Reads the CSV file and stores the information in the towers array */
+tower_t **readTowers(tower_t **towers, FILE *datasetFile, int *numTowers);
+
+/* Reads the current row from the CSV and converts it into a new tower */
+void readCurrentTower(char *lineBuffer, tower_t *tower);
+
+/* Frees all towers in a towers array */
+void freeTowers(tower_t **towers, int numTowers);
+
+#endif

voronoi.c

@@ -2,7 +2,7 @@
  *
  * Created by Rory Healy (healyr@student.unimelb.edu.au)
  * Created on 12th August 2021
- * Last modified 9th September 2021
+ * Last modified 11th September 2021
  *
  * Contains functions involving the generation of the Voronoi diagram, and 
  * running each stage of the assignment.
@@ -17,101 +17,9 @@
 #include "voronoi.h"
 #endif
 
-#define BASE_10 10
-#define MAX_CSV_ENTRY_LEN 512
-#define MAX_FIELD_LEN 128
-#define NUM_CSV_FIELDS 6
-
-tower_t **readTowers(tower_t **towers, FILE *datasetFile, int *numTowers) {
-    /* Maximum length of a single CSV line */
-    size_t lineBufferSize = MAX_CSV_ENTRY_LEN + 1;
-
-    /* Stores the current line from the CSV */
-    char *lineBuffer = malloc(lineBufferSize * sizeof(*lineBuffer));
-    checkNullPointer(lineBuffer);
-
-    int maxSizetowers = 1;
-
-    /* Discard the header line, then read the rest of the CSV */
-    getline(&lineBuffer, &lineBufferSize, datasetFile);
-    while (getline(&lineBuffer, &lineBufferSize, datasetFile) > 0) {
-        /* Check if there enough space in the towers array */
-        if (*numTowers == maxSizetowers) {
-            maxSizetowers *= 2;
-            tower_t **temp = realloc(towers, maxSizetowers * sizeof(*towers));
-            checkNullPointer(temp);
-            towers = temp;
-        }
-
-        /* The current tower being filled in with information */
-        towers[*numTowers] = malloc(sizeof(*towers[*numTowers]));
-
-        readCurrentTower(lineBuffer, towers[*numTowers]);
-        *numTowers += 1;    
-    }
-    free(lineBuffer);
-    return towers;
-}
-
-void readCurrentTower(char *lineBuffer, tower_t *tower) {
-    /* Stores the current CSV field for the current line */
-    char *token = strtok(lineBuffer, ",");
-    size_t tokenLength;
-
-    for (int i = 0; i < NUM_CSV_FIELDS; i++) {
-        tokenLength = strlen(token);
-        switch(i) {
-            /* Case 0, 1, and 3 deal with strings
-             * Case 2 deals with an integer
-             * Case 4 and 5 deal with doubles
-             * Each case is handled seperately to fill in the
-             * tower with no space wasted.
-             */
-            case 0:
-                tower->id = malloc(sizeof(char) * tokenLength + 1);
-                checkNullPointer(tower->id);
-                strcpy(tower->id, token);
-                tower->id[tokenLength] = '\0';
-                break;
-            case 1:
-                tower->postcode = malloc(sizeof(char) * tokenLength + 1);
-                checkNullPointer(tower->postcode);
-                strcpy(tower->postcode, token);
-                tower->postcode[tokenLength] = '\0';
-                break;
-            case 2:
-                tower->population = strtol(token, NULL, BASE_10);
-                break;
-            case 3:
-                tower->manager = malloc(sizeof(char) * tokenLength + 1);
-                checkNullPointer(tower->manager);
-                strcpy(tower->manager, token);
-                tower->manager[tokenLength] = '\0';
-                break;
-            case 4:
-                tower->x = strtod(token, NULL);
-                break;
-            case 5:
-                tower->y = strtod(token, NULL);
-                break;
-        }
-        token = strtok(NULL, ",");
-    }
-}
-
-void freeTowers(tower_t **towers, int numTowers) {
-    for (int i = 0; i < numTowers; i++) {
-        free(towers[i]->id);
-        free(towers[i]->manager);
-        free(towers[i]->postcode);
-        free(towers[i]);
-    }
-    free(towers);
-}
-
 vertex_t **readPoints(vertex_t **points, FILE *pointsFile, int *numPoints) {
-    /* Current length of a single points line */
-    size_t lineBufferSize = 50;
+    /* Initial size of buffer is 1 as getline() reallocs as needed */
+    size_t lineBufferSize = 1;
 
     /* Stores the current line from the points file */
     char *lineBuffer = malloc(lineBufferSize * sizeof(*lineBuffer));
@@ -148,6 +56,16 @@ vertex_t **readPoints(vertex_t **points, FILE *pointsFile, int *numPoints) {
     return points;
 }
 
+void stage1PrintBisector(bisector_t *bisector, FILE *outputFile) {
+    if (bisector->isSlopeInfinite) {
+        /* Cannot print infinite slope, so print only x-intercept */
+        fprintf(outputFile, "x = %lf\n", bisector->midX);
+    } else {
+        fprintf(outputFile, "y = %lf * (x - %lf) + %lf\n", \
+            bisector->slope, bisector->midX,  bisector->midY);
+    }
+}
+
 void freePoints(vertex_t **points, int numPoints) {
     for (int i = 0; i < numPoints; i++) {
         free(points[i]);
@@ -168,17 +86,12 @@ void stage1(char *pointsFileName, char *outputFileName) {
 
     /* For each pair, calculate and print the bisector to outputFile */
     for (int i = 0; i < numPoints; i += 2) {
-        bisector_t currBisector = getBisector(points[i], points[i + 1]);
-
-        /* Cannot print infinite slope, so print only x-intercept */
-        if (currBisector.isSlopeInfinite) {
-            fprintf(outputFile, "x = %lf\n", currBisector.x);
-        } else {
-            fprintf(outputFile, "y = %lf * (x - %lf) + %lf\n", \
-                currBisector.slope, currBisector.x,  currBisector.y);
-        }
+        bisector_t *currBisector = getBisector(points[i], points[i + 1]);
+        stage1PrintBisector(currBisector, outputFile);
+        free(currBisector);
     }
 
+    /* Clean up */
     freePoints(points, numPoints);
     fclose(pointsFile);
     fclose(outputFile);
@@ -190,8 +103,21 @@ void stage2(char *pointsFileName, char *polygonFileName, char *outputFileName) {
     polygonFile = safeFileOpen(&polygonFile, polygonFileName, "r");
     outputFile = safeFileOpen(&outputFile, outputFileName, "w");
 
+    /* Points are given as pairs, so initialise 2 points */
+    vertex_t **points = malloc(sizeof(*points) * 2);
+    checkNullPointer(points);
+    int numPoints = 0;
+    points = readPoints(points, pointsFile, &numPoints);
+
+    /* Construct the DCEL from the polygon file */
+    DCEL_t *dcel = readPolygonFile(polygonFileName);
+
+    /* Calculate and print intersections to the output file */
     
 
+    /* Clean up */
+    freePoints(points, numPoints);
+    freeDCEL(dcel);
     fclose(pointsFile);
     fclose(polygonFile);
     fclose(outputFile);
@@ -205,6 +131,7 @@ void stage3(char *dataFileName, char *polygonFileName, char *outputFileName) {
 
 
 
+    /* Clean up */
     fclose(dataFile);
     fclose(polygonFile);
     fclose(outputFile);
@@ -217,7 +144,8 @@ void stage4(char *dataFileName, char *polygonFileName, char *outputFileName) {
     outputFile = safeFileOpen(&outputFile, outputFileName, "w");
 
 
-    
+
+    /* Clean up */
     fclose(dataFile);
     fclose(polygonFile);
     fclose(outputFile);

voronoi.h

@@ -5,27 +5,12 @@
 #ifndef VORONOI_HEADER
 #define VORONOI_HEADER
 
-typedef struct tower {
-    char *id;
-    char *postcode;
-    char *manager;
-    int population;
-    double x;
-    double y;
-} tower_t;
-
-/* Reads the CSV file and stores the information in the towers array */
-tower_t **readTowers(tower_t **towers, FILE *datasetFile, int *numTowers);
-
-/* Reads the current row from the CSV and converts it into a new tower */
-void readCurrentTower(char *lineBuffer, tower_t *tower);
-
-/* Frees all towers in a towers array */
-void freeTowers(tower_t **towers, int numTowers);
-
 /* Reads a points file and stores the information in the points array */
 vertex_t **readPoints(vertex_t **points, FILE *pointsFile, int *numPoints);
 
+/* Prints bisectors to an output file */
+void stage1PrintBisector(bisector_t *bisector, FILE *outputFile);
+
 /* Frees all points from a points array */
 void freePoints(vertex_t **points, int numPoints);