DB Physics Arithmeticam

This software is published under the GNU General Public License v3.0.

Internal movement of a quark.

Coding the dimensional basic

The separate fundamental forces of nature: – the strong interaction, the electromagnetic interaction, the weak interaction and the gravitational interaction – are calculatable with one formula out of one principle. The statistical math of the quantum theory is set aside in favor of a goniometric approach. Gravitation is the only force that matters and the strong force, the electromagnetic force and the weak force can be explained out of gravitation, while gravity itself is only caused by the curvature of a mass, corresponding with a certain amount of bending of spacetime.

The axiom is that the most elementary particle in existence is the dimensional basic (db or

). The

itself has no dimensions (no length, no width and no height). The

is found everywhere in the universe and is always moving through spacetime, where the speed of the movement of the

, in respect to its surroundings, can have any value. The curvature of space on the location of the

is infinite while time on the location of the

stands still. The

behaves like a black hole without dimensions. The

is the building block of all that we perceive.

The formula for the extent of spacetime curvature around a

is:

In the formula: x, y, z, are coordinates in spacetime [m], Kr = curvature [m^-1].

Formula (0) describes the relative lessened extent of curvature of spacetime surrounding the

.

The distance between the various

s varies in time by movements relative to each other. The direction of movement is being influenced according to gravitational laws. The tracks of movement are being influenced by the curvature of spacetime caused by the

s themselves. This means that spacetime surrounding a

gets smaller when the

s are approaching each other while spacetime surrounding a

gets bigger when the

s move away from each other.

The

is different than other particles in that respect that other particles consist out of multiple

s while the

itself is a singular particle. Each

is a singularity (infinite curvature) on itself while other particles than the

are a combination of multiple

s and thus a system of multiple singularities.

The observed forces (strong, electromagnetic, weak and gravitation) have the same origin. The cause of these forces are because of the characteristics of a singular

. The observed forces are in fact a sum of circular movements that come to exist when multiple

s interact with each other.

Figure 1: The tracks of two interacting

s on different distances from each other.
(Original: Deflection of the tracks of a photon close to an object with a heavy mass).

In figure 1 is shown how the movement tracks of photons react to the event horizon of a black hole. The same regularity applies to a binary black hole system. This is equal to the movement tracks of two

s in respect to each other with the difference that the two

s have no event horizon. The Pauli principle is never violated because the

s have no dimensions, they can approach each other, but can never touch each other. These movement tracks are equal in behavior to Newton’s laws of gravity. On the basis of that information the Borland C computer program ‘Newton’ has been developed. This computer program shows the movement tracks of

s in three dimensional spacetime, in which the movement tracks of the

s follow the gravitational laws. A three dimensional snapshot with nine interacting

s is shown in figure 2. In this figure the Einsteinian bending of spacetime has not been taken into account. The computer program ‘Newton’ gives the possibility to show the time delay in video, as seen by an outside observer thus making clear the principle of time delay.

Figure 2: The movement tracks of nine

s during a random time.

The second model that has been developed is the Borland C computer plot program ‘Einstein’. This computer program has been developed to show how spacetime around a

is being bend as seen by an outside observer, the extent of bending calculated according to formula (0).br>
Just like one

as a singular singularity causes bending of spacetime because of an infinite curvature, a multitude of

s will show a stronger bending of spacetime because of a sum of infinite curvatures. As Einstein made clear, we can speak of curbed spacetime instead of linear spacetime. The more mass an object has, the more spacetime bends. In fact mass is the sum of the curvatures of a certain amount of

s close to each other. In case of for example three billion

s one can speak of three billion times infinite curvature. This makes it possible to isolate infinite numbers in comparison equations and thus mass can be expressed as an absolute number. One can say that a cluster of a certain amount of

s will have an absolute number of infinite curvatures. In this way one can speak of mass A with X times infinite curvatures, while mass B has Y times infinite curvatures. The infinities on both sides of the comparison can be done away with and only the absolute proportions of X and Y remain for the respective masses. A cluster of

s with an absolute amount of

s correlates with the mass of an object and thus a certain extent of bending of spacetime.

The extent of bending of spacetime is calculated using formula (0), where the extent of curvature on a specific position of spacetime is being calculated. A bigger curvature means that spacetime is more bended, whereas a smaller curvature means that spacetime is less bended.

An example of this is shown in figure 3. In figure 3 the plot of a cube of spacetime is shown. The Einsteinian bending of a cube of spacetime is made visual. While figure 3a shows no bending of spacetime because of the absence of a

, the bending in a cube of spacetime, and thus deformed distances for an outside observer, in figure 3b have been calculated according to formula (0) because of the position of a

in the center of the cube of spacetime. At the center of the six surfaces of the cube of spacetime the distance to the

is the smallest, for the outside observer it appears that that piece of spacetime is closer to the

than it should be in linear (uncurbed) spacetime, this because of the bending of spacetime, made visual by formula (0). Hence the pointy form of the corners of the cube of spacetime, there the distance to the

is the biggest. Because of the bending of spacetime the distance is bigger for the outside observer than it should be according to a linear scale, this again made visual by calculating the extent of bending of spacetime according to formula (0). The closer spacetime is to a

, the higher the curvature and the more spacetime will be bend.

Figure 3: The bending of a cube of spacetime under the influence of a

3a. Uncurbed (linear) cube of spacetime. 3b. Cube of spacetime curbed by the presence of a in the center.

Conclusion: The Newtonian laws represent the straight movement paths as being caused by the bending of spacetime, just like Einstein made clear. Thus Newton’s laws of gravity apply to the movement paths of the

or a multitude of

s.
Both computer programs together represent the movement and character of the

. The reality of the

can be simulated by computer programs according to gravitational laws, taking into account the reality of formula (0) and the thereby caused bending of spacetime, with, as seen by an outside observer, the observed bending of spacetime and time delay. A third model, combining the linear Newtonian laws of gravity with Einsteinian bending of space and delay of time should be able to simulate the universe as a whole. Whereas a model with an infinite amount of

s is practically not possible, a model with a subset of a large number of

s should be possible.

Below the sources codes of the Borland C computer programs ‘Newton’ and ‘Einstein’ can be seen, while not making a choice shows a MS Quick Basic example of

movement analysis with which figure 2 has been calculated.

Download article (PDF):
Coding the dimensional basic

Download code (TXT):
dbmove.bas newton.cpp einstein.cpp

Show code:
Program Newton Program Einstein

Borland C Program Newton:

0	// (C) 1996 G.J. Smit, Nijmegen, Nederland
1	// This software is published under the GNU General Public License v3.0
2	// www.dbphysics.com
3	// The program 'Newton' is a n-body model where simultaneously for the positions of multiple dimensional basics (theoretical infinite curvature) moving through space time interact with each other according to newtonian laws.
4
5	#include
6	#include
7	#include
8	#include
9	#include
10	#include
11	#include
12
13	FILE *bestand; // Pointer voor geopend bestand.
14	char b_naam[12]; // Naam van actief bestand.
15	char b_test; // Controle voor bestaan bestand.
16	char toets; // Variabele voor ingedrukte toets.
17	int t1,t2,t3,t4; // Tellers voor lussen.
18	int stap,dim,deel; // Aantal stappen, dimensies en deeltjes.
19	int spoor; // Lengte afbeelding in tijd per deeltje.
20	int prog; // Programma einde.
21	int i_temp; // Tijdelijk opslag integer.
22	int midd; // Middelpunt in tekening aan/uit.
23	int modus; // Kleur per deel/diepte.
24	float w_g, w_x, w_y; // Windowgrootte, x en y co�rdinaatgrootte.
25	float x_max, y_max; // Aantal pixels op beeldscherm.
26	float t_frag, grens; // Tijdfragmentatie en grenswaarde ruimte.
27	float r_o, r_n; // Bereik willekeurige beginco�rdinaten.
28	float fzx, fzy, fzz; // Zwaartekracht per as.
29	float g_temp; // Grenswaarde wisseling.
30	float f_temp; // Tijdelijk opslag float.
31	float midx, midy; // Middelpunt berekening-variabelen.
32	float diepte; // Kleur-diepte variabele.
33	float huge x3[251][4]; // Maximaal 250 x3d-co�rdinaten.
34	float huge y3[251][4]; // Maximaal 250 y3d-co�rdinaten.
35	float huge z3[251][4]; // Maximaal 250 z3d-co�rdinaten.
36	float huge x2[251][30]; // Maximaal 30 x2d-co�rdinaten per deeltje.
37	float huge y2[251][30]; // Maximaal 30 y2d-co�rdinaten per deeltje.
38
39	void theorie(void) // Rekenkundig variabele verhoudingen.
40	{ detectgraph(&t1, &t2);
41	initgraph(&t1, &t2, "..\\bgi");
42	setcolor(7);
43	for(t1=0; t1<20; t1++)
44	{ line(x_max/2+200-t110, y_max/2, x_max/2, y_max/2+t110);
45	line(x_max/2-t110, y_max/2, x_max/2, y_max/2+200-t110);
46	line(x_max/2-200+t110, y_max/2, x_max/2, y_max/2-t110);
47	line(x_max/2+t110, y_max/2, x_max/2, y_max/2-200+t110);
48	}
49	getch();
50	closegraph();
51	}
52
53	void varbestand(void) // Variabele waarden bestand inlezen.
54	{ bestand=fopen(b_naam,"r");
55	if(bestand==NULL) b_test=0;
56	else
57	{ fscanf(bestand, "%d%d%f%f%f%f", &stap, &deel, &r_o, &r_n, &t_frag, &grens);
58	if(grens!=0) w_g=1.5*grens;
59	b_test=1;
60	}
61	fclose(bestand);
62	}
63
64	void menuopbeeld(void)
65	{ clrscr();
66	textcolor(10);
67	printf("[b]estandsnaam ");
68	if(b_test==0) printf("-"); else printf("+");
69	printf(" : %s\n\n", b_naam);
70	printf("[c]o�rdinaten\n");
71	printf("[w]illekeur : %f\n", r_o);
72	printf("[r]ichting : %f\n\n", r_n);
73	printf("[t]ijdfragmentatie : %f\n", t_frag);
74	printf("[g]rens : %f\n\n", grens);
75	printf("[s]tappen : %d\n", stap);
76	printf("[d]eel : %d\n\n", deel);
77	printf("[v]enster : %f\n", w_g);
78	printf("[p]rojectie : %d\n", spoor);
79	printf("[m]iddelpunt : ");
80	if(midd==0) printf("uit\n"); else printf("aan\n");
81	printf("[k]leurmodus : ");
82	if(modus==0) printf("deel\n\n\n"); else printf("diepte\n\n\n");
83	printf("[R]ekenen [E]n [T]ekenen [S]toppen\n\n");
84	}
85
86	void menuvraag(void)
87	{ toets=getch();
88	if(toets==98) { printf("Nieuwe bestandsnaam? ");
89	scanf("%s", &b_naam); }
90	if(toets==99) { printf("Invoer co�rdinaten, nog programmeren...");
91	getch(); }
92	if(toets==119) { f_temp=r_o; printf("Maximale willekeur? ");
93	scanf("%f", &r_o);
94	if(r_o<0\|\|r_o==0\|\|r_o>30000) r_o=f_temp; }
95	if(toets==114) { f_temp=r_n; printf("Maximale richting? ");
96	scanf("%f", &r_n);
97	if(r_n<0\|\|r_o==0\|\|r_o>2500) r_o=f_temp; }
98	if(toets==116) { f_temp=t_frag; printf("Nieuwe tijdfragmentatie? ");
99	scanf("%f", &t_frag);
100	if(t_frag<0\|\|t_frag==0\|\|t_frag>1) t_frag=f_temp; }
101	if(toets==103) { f_temp=grens; printf("Grens van ruimte? ");
102	scanf("%f", &grens);
103	if(grens<0\|\|grens>32500) grens=f_temp; }
104	if(toets==115) { i_temp=stap; printf("Aantal stappen? ");
105	scanf("%d", &stap);
106	if(stap<1\|\|stap>32500) stap=i_temp; }
107	if(toets==100) { i_temp=deel; printf("Aantal deeltjes? ");
108	scanf("%d", &deel);
109	if(deel<2\|\|deel>250) deel=i_temp; }
110	if(toets==118) { f_temp=w_g; printf("Venstergrootte? ");
111	scanf("%f", &w_g);
112	if(w_g<0\|\|w_g==0\|\|w_g>32500) w_g=f_temp; }
113	if(toets==112) { i_temp=spoor; printf("Aantal fragmenten? ");
114	scanf("%d", &spoor);
115	if(spoor<0\|\|spoor>30) spoor=i_temp; }
116	if(toets==109) { if(midd==0) midd=1; else midd=0; }
117	if(toets==107) { if(modus==0) modus=1; else modus=0; }
118	}
119
120	void willekeur(void)
121	{ for(t1=0;t1
122	{ x3[t1][0]=2(random(32767)r_o/32767)-r_o;
123	y3[t1][0]=2(random(32767)r_o/32767)-r_o;
124	z3[t1][0]=2(random(32767)r_o/32767)-r_o;
125	x3[t1][1]=x3[t1][0]+2(random(32767)r_n/32767)-r_n;
126	y3[t1][1]=y3[t1][0]+2(random(32767)r_n/32767)-r_n;
127	z3[t1][1]=z3[t1][0]+2(random(32767)r_n/32767)-r_n;
128	}
129	}
130
131	void reken(void) // Kaal [R]ekenen, snelste routine.
132	{ // Bestand voor co�rdinaten openen.
133	bestand=fopen(b_naam,"w");
134	fprintf(bestand, "%d %d %f %f %f %f", stap, deel, r_o, r_n, t_frag, grens);
135	for(t1=0;t1
136	fprintf(bestand, " %f %f %f", x3[t1][1], y3[t1][1], z3[t1][1]);
137
138	// Co�rdinaten berekenen, schrijven naar disk en naar tekst-beeldscherm.
139	for(t1=0;t1
140	{ for(t2=0;t2
141	{ x3[t2][3]=0;
142	y3[t2][3]=0;
143	z3[t2][3]=0;
144	}
145	for(t2=0;t2
146	{ x3[t2][2]=x3[t2][1]-x3[t2][0];
147	y3[t2][2]=y3[t2][1]-y3[t2][0];
148	z3[t2][2]=z3[t2][1]-z3[t2][0];
149	for(t3=t2;t3
150	{ fzx=x3[t3][1]-x3[t2][1];
151	fzy=y3[t3][1]-y3[t2][1];
152	fzz=z3[t3][1]-z3[t2][1];
153	if(fzx!=0) { fzx=1/fzx; x3[t2][3]=x3[t2][3]+fzx;
154	x3[t3][3]=x3[t3][3]-fzx; }
155	if(fzy!=0) { fzy=1/fzy; y3[t2][3]=y3[t2][3]+fzy;
156	y3[t3][3]=y3[t3][3]-fzy; }
157	if(fzz!=0) { fzz=1/fzz; z3[t2][3]=z3[t2][3]+fzz;
158	z3[t3][3]=z3[t3][3]-fzz; }
159	}
160	x3[t2][0]=x3[t2][1];
161	y3[t2][0]=y3[t2][1];
162	z3[t2][0]=z3[t2][1];
163	x3[t2][1]=x3[t2][0]+x3[t2][2]+x3[t2][3];
164	y3[t2][1]=y3[t2][0]+y3[t2][2]+y3[t2][3];
165	z3[t2][1]=z3[t2][0]+z3[t2][2]+z3[t2][3];
166	}
167	for(t2=0;t2
168	fprintf(bestand, " %f %f %f", x3[t2][1], y3[t2][1], z3[t2][1]);
169	putchar(13); printf("%d",t1+1);
170	}
171	fclose(bestand);
172	b_test=1;
173	}
174
175	void rekenmetopties(void) // [R]ekenen met grens en/of t_frag aan.
176	{ // Bestand voor co�rdinaten openen.
177	bestand=fopen(b_naam,"w");
178	fprintf(bestand, "%d %d %f %f %f %f", stap, deel, r_o, r_n, t_frag, grens);
179	for(t1=0;t1
180	fprintf(bestand, " %f %f %f", x3[t1][1], y3[t1][1], z3[t1][1]);
181
182	// Co�rdinaten berekenen, schrijven naar disk en naar tekst-beeldscherm.
183	for(t1=0;t1
184	{ for(t2=0;t2
185	{ x3[t2][3]=0;
186	y3[t2][3]=0;
187	z3[t2][3]=0;
188	}
189	for(t2=0;t2
190	{ x3[t2][2]=x3[t2][1]-x3[t2][0];
191	y3[t2][2]=y3[t2][1]-y3[t2][0];
192	z3[t2][2]=z3[t2][1]-z3[t2][0];
193	for(t3=t2;t3
194	{ fzx=x3[t3][1]-x3[t2][1];
195	fzy=y3[t3][1]-y3[t2][1];
196	fzz=z3[t3][1]-z3[t2][1];
197	if(fzx!=0) { fzx=1/fzx; x3[t2][3]=x3[t2][3]+fzx;
198	x3[t3][3]=x3[t3][3]-fzx; }
199	if(fzy!=0) { fzy=1/fzy; y3[t2][3]=y3[t2][3]+fzy;
200	y3[t3][3]=y3[t3][3]-fzy; }
201	if(fzz!=0) { fzz=1/fzz; z3[t2][3]=z3[t2][3]+fzz;
202	z3[t3][3]=z3[t3][3]-fzz; }
203	}
204	// Bewerk co�rdinaten als t_frag ongelijk aan 1.
205	if(t_frag!=1)
206	{ x3[t2][2]=x3[t2][2]t_frag; x3[t2][3]=x3[t2][3]t_frag;
207	y3[t2][2]=y3[t2][2]t_frag; y3[t2][3]=y3[t2][3]t_frag;
208	z3[t2][2]=z3[t2][2]t_frag; z3[t2][3]=z3[t2][3]t_frag;
209	}
210	// Bepaal de nieuwe co�rdinaten.
211	x3[t2][0]=x3[t2][1];
212	y3[t2][0]=y3[t2][1];
213	z3[t2][0]=z3[t2][1];
214	x3[t2][1]=x3[t2][0]+x3[t2][2]+x3[t2][3];
215	y3[t2][1]=y3[t2][0]+y3[t2][2]+y3[t2][3];
216	z3[t2][1]=z3[t2][0]+z3[t2][2]+z3[t2][3];
217	// Test grensoverschrijding.
218	if(grens>0)
219	{ if(x3[t2][1]<-grens\|\|x3[t2][1]>grens)
220	{ g_temp=x3[t2][1]; x3[t2][1]=-x3[t2][0]; x3[t2][0]=-g_temp; }
221	if(y3[t2][1]<-grens\|\|y3[t2][1]>grens)
222	{ g_temp=y3[t2][1]; y3[t2][1]=-y3[t2][0]; y3[t2][0]=-g_temp; }
223	if(z3[t2][1]<-grens\|\|z3[t2][1]>grens)
224	{ g_temp=z3[t2][1]; z3[t2][1]=-z3[t2][0]; z3[t2][0]=-g_temp; }
225	}
226	}
227	for(t2=0;t2
228	fprintf(bestand, " %f %f %f", x3[t2][1], y3[t2][1], z3[t2][1]);
229	putchar(13); printf("%d",t1+1);
230	}
231	fclose(bestand);
232	b_test=1;
233	}
234
235	void rekenenteken(void) // [E]n.
236	{ detectgraph(&t1, &t2);
237	initgraph(&t1, &t2, "..\\bgi");
238	w_x=(x_max+1)/(w_g2); w_y=(y_max+1)/(w_g2);
239	printf(" \|%d\|%d\|%f\|%f\|%f\|%f\|%f\|%d\|%s",
240	stap, deel, r_o, r_n, t_frag, grens, w_g, spoor, b_naam);
241	gotoxy(0,0);
242	midd=0; spoor=0; modus=0;
243
244	// Bestand voor co�rdinaten openen.
245	bestand=fopen(b_naam,"w");
246	fprintf(bestand, "%d %d %f %f %f %f", stap, deel, r_o, r_n, t_frag, grens);
247	for(t1=0;t1
248	fprintf(bestand, " %f %f %f", x3[t1][1], y3[t1][1], z3[t1][1]);
249
250	// Co�rdinaten berekenen, schrijven naar disk en naar grafisch beeldscherm.
251	for(t1=0;t1
252	{ for(t2=0;t2
253	{ x3[t2][3]=0;
254	y3[t2][3]=0;
255	z3[t2][3]=0;
256	}
257	for(t2=0;t2
258	{ x3[t2][2]=x3[t2][1]-x3[t2][0];
259	y3[t2][2]=y3[t2][1]-y3[t2][0];
260	z3[t2][2]=z3[t2][1]-z3[t2][0];
261	for(t3=t2;t3
262	{ fzx=x3[t3][1]-x3[t2][1];
263	fzy=y3[t3][1]-y3[t2][1];
264	fzz=z3[t3][1]-z3[t2][1];
265	if(fzx!=0) { fzx=1/fzx; x3[t2][3]=x3[t2][3]+fzx;
266	x3[t3][3]=x3[t3][3]-fzx; }
267	if(fzy!=0) { fzy=1/fzy; y3[t2][3]=y3[t2][3]+fzy;
268	y3[t3][3]=y3[t3][3]-fzy; }
269	if(fzz!=0) { fzz=1/fzz; z3[t2][3]=z3[t2][3]+fzz;
270	z3[t3][3]=z3[t3][3]-fzz; }
271	}
272	// Bewerk co�rdinaten als t_frag ongelijk aan 1.
273	if(t_frag!=1)
274	{ x3[t2][2]=x3[t2][2]t_frag; x3[t2][3]=x3[t2][3]t_frag;
275	y3[t2][2]=y3[t2][2]t_frag; y3[t2][3]=y3[t2][3]t_frag;
276	z3[t2][2]=z3[t2][2]t_frag; z3[t2][3]=z3[t2][3]t_frag;
277	}
278	// Bepaal de nieuwe co�rdinaten.
279	x3[t2][0]=x3[t2][1];
280	y3[t2][0]=y3[t2][1];
281	z3[t2][0]=z3[t2][1];
282	x3[t2][1]=x3[t2][0]+x3[t2][2]+x3[t2][3];
283	y3[t2][1]=y3[t2][0]+y3[t2][2]+y3[t2][3];
284	z3[t2][1]=z3[t2][0]+z3[t2][2]+z3[t2][3];
285	// Test grensoverschrijding.
286	if(grens>0)
287	{ if(x3[t2][1]<-grens\|\|x3[t2][1]>grens)
288	{ g_temp=x3[t2][1]; x3[t2][1]=-x3[t2][0]; x3[t2][0]=-g_temp; }
289	if(y3[t2][1]<-grens\|\|y3[t2][1]>grens)
290	{ g_temp=y3[t2][1]; y3[t2][1]=-y3[t2][0]; y3[t2][0]=-g_temp; }
291	if(z3[t2][1]<-grens\|\|z3[t2][1]>grens)
292	{ g_temp=z3[t2][1]; z3[t2][1]=-z3[t2][0]; z3[t2][0]=-g_temp; }
293	}
294	}
295	for(t2=0;t2
296	fprintf(bestand, " %f %f %f", x3[t2][1], y3[t2][1], z3[t2][1]);
297	for(t2=0;t2
298	{ x2[t2][0]=y3[t2][1]-.5*x3[t2][1];
299	y2[t2][0]=z3[t2][1]+.5*x3[t2][1];
300	x2[t2][0]=x_max/2-w_x*x2[t2][0];
301	y2[t2][0]=y_max/2-w_y*y2[t2][0];
302	putpixel(x2[t2][0],y2[t2][0],2+t2);
303	}
304	putchar(13); printf("%d",t1+1);
305	}
306	putchar(13); printf("Klaar");
307	fclose(bestand);
308	b_test=1;
309	getch();
310	closegraph();
311	}
312
313	void geendisk(void) // [A]lleen rekenen en tekenen.
314	{ detectgraph(&t1, &t2);
315	initgraph(&t1, &t2, "..\\bgi");
316	w_x=(x_max+1)/(w_g2); w_y=(y_max+1)/(w_g2);
317	if(modus!=0) diepte=255/(w_g*2);
318
319	printf(" \|%d\|%d\|%f\|%f\|%f\|%f\|%f\|%d\|XXXXXX",
320	stap, deel, r_o, r_n, t_frag, grens, w_g, spoor);
321	gotoxy(0,0);
322
323	// Co�rdinaten berekenen, schrijven naar grafisch beeldscherm.
324	for(t1=0;t1
325	{ for(t2=0;t2
326	{ x3[t2][3]=0;
327	y3[t2][3]=0;
328	z3[t2][3]=0;
329	}
330	putchar(13);printf("%d", t1);
331	if(midd>0) { midx=0; midy=0; }
332	for(t2=0;t2
333	{ x3[t2][2]=x3[t2][1]-x3[t2][0];
334	y3[t2][2]=y3[t2][1]-y3[t2][0];
335	z3[t2][2]=z3[t2][1]-z3[t2][0];
336	for(t3=t2;t3
337	{ fzx=x3[t3][1]-x3[t2][1];
338	fzy=y3[t3][1]-y3[t2][1];
339	fzz=z3[t3][1]-z3[t2][1];
340	if(fzx!=0) { fzx=1/fzx; x3[t2][3]=x3[t2][3]+fzx;
341	x3[t3][3]=x3[t3][3]-fzx; }
342	if(fzy!=0) { fzy=1/fzy; y3[t2][3]=y3[t2][3]+fzy;
343	y3[t3][3]=y3[t3][3]-fzy; }
344	if(fzz!=0) { fzz=1/fzz; z3[t2][3]=z3[t2][3]+fzz;
345	z3[t3][3]=z3[t3][3]-fzz; }
346	}
347	// Bewerk co�rdinaten als t_frag ongelijk aan 1.
348	if(t_frag!=1)
349	{ x3[t2][2]=x3[t2][2]t_frag; x3[t2][3]=x3[t2][3]t_frag;
350	y3[t2][2]=y3[t2][2]t_frag; y3[t2][3]=y3[t2][3]t_frag;
351	z3[t2][2]=z3[t2][2]t_frag; z3[t2][3]=z3[t2][3]t_frag;
352	}
353	// Bepaal de nieuwe co�rdinaten.
354	x3[t2][0]=x3[t2][1];
355	y3[t2][0]=y3[t2][1];
356	z3[t2][0]=z3[t2][1];
357	x3[t2][1]=x3[t2][0]+x3[t2][2]+x3[t2][3];
358	y3[t2][1]=y3[t2][0]+y3[t2][2]+y3[t2][3];
359	z3[t2][1]=z3[t2][0]+z3[t2][2]+z3[t2][3];
360	// Test grensoverschrijding.
361	if(grens>0)
362	{ if(x3[t2][1]<-grens\|\|x3[t2][1]>grens)
363	{ g_temp=x3[t2][1]; x3[t2][1]=-x3[t2][0]; x3[t2][0]=-g_temp; }
364	if(y3[t2][1]<-grens\|\|y3[t2][1]>grens)
365	{ g_temp=y3[t2][1]; y3[t2][1]=-y3[t2][0]; y3[t2][0]=-g_temp; }
366	if(z3[t2][1]<-grens\|\|z3[t2][1]>grens)
367	{ g_temp=z3[t2][1]; z3[t2][1]=-z3[t2][0]; z3[t2][0]=-g_temp; }
368	}
369	}
370	for(t2=0;t2
371	{ x2[t2][0]=y3[t2][1]-.5*x3[t2][1];
372	y2[t2][0]=z3[t2][1]+.5*x3[t2][1];
373	if(midd>0)
374	{ midx=midx+x2[t2][0];
375	midy=midy+y2[t2][0];
376	}
377	}
378	if(midd>0) { midx=midx/deel; midy=midy/deel; }
379	for(t2=0;t2
380	{ if(midd>0)
381	{ x2[t2][0]=x_max/2+midx-w_x*x2[t2][0];
382	y2[t2][0]=y_max/2+midy-w_y*y2[t2][0];
383	}
384	else
385	{ x2[t2][0]=x_max/2-w_x*x2[t2][0];
386	y2[t2][0]=y_max/2-w_y*y2[t2][0];
387	}
388	if(modus==0) putpixel(x2[t2][0],y2[t2][0],2+t2);
389	else putpixel(x2[t2][0],y2[t2][0],1+(x3[t2][1]+w_g)*diepte);
390	if(spoor>0)
391	{ if(t1
392	{ x2[t2][spoor-1-t1]=x2[t2][0]; y2[t2][spoor-1-t1]=y2[t2][0]; }
393	else
394	{ putpixel(x2[t2][spoor-1],y2[t2][spoor-1],0);
395	for(t3=spoor-1;t3>0;t3--)
396	{ x2[t2][t3]=x2[t2][t3-1]; y2[t2][t3]=y2[t2][t3-1]; }
397	}
398	}
399	}
400	putchar(13); printf("%d",t1+1);
401	}
402	putchar(13); printf("Klaar");
403	getch();
404	closegraph();
405	}
406
407	void teken(void)
408	{ detectgraph(&t1, &t2);
409	initgraph(&t1, &t2, "..\\bgi");
410	// Berekenen hoeveelheid pixels per ��nheid.
411	w_x=(x_max+1)/(w_g2); w_y=(y_max+1)/(w_g2);
412
413	bestand=fopen(b_naam,"r");
414	fscanf(bestand, "%d%d%f%f%f%f", &stap, &deel, &r_o, &r_n, &t_frag, &grens);
415	printf(" \|%d\|%d\|%f\|%f\|%f\|%f\|%f\|%d\|%s",
416	stap, deel, r_o, r_n, t_frag, grens, w_g, spoor, b_naam);
417
418	if(modus!=0) diepte=255/(w_g*2);
419	for(t1=0;t1
420	{ putchar(13);printf("%d", t1);
421	if(midd>0) { midx=0; midy=0; }
422	for(t2=0;t2
423	fscanf(bestand, "%f%f%f", &x3[t2][1], &y3[t2][1], &z3[t2][1]);
424	for(t2=0;t2
425	{ x2[t2][0]=y3[t2][1]-.5*x3[t2][1];
426	y2[t2][0]=z3[t2][1]+.5*x3[t2][1];
427	if(midd>0)
428	{ midx=midx+x2[t2][0];
429	midy=midy+y2[t2][0];
430	}
431	}
432	if(midd>0) { midx=midx/deel; midy=midy/deel; }
433	for(t2=0;t2
434	{ if(midd>0)
435	{ x2[t2][0]=x_max/2+midx-w_x*x2[t2][0];
436	y2[t2][0]=y_max/2+midy-w_y*y2[t2][0];
437	}
438	else
439	{ x2[t2][0]=x_max/2-w_x*x2[t2][0];
440	y2[t2][0]=y_max/2-w_y*y2[t2][0];
441	}
442	if(modus==0) putpixel(x2[t2][0],y2[t2][0],2+t2);
443	else putpixel(x2[t2][0],y2[t2][0],1+(x3[t2][1]+w_g)*diepte);
444	if(spoor>0)
445	{ if(t1
446	{ x2[t2][spoor-1-t1]=x2[t2][0]; y2[t2][spoor-1-t1]=y2[t2][0]; }
447	else
448	{ putpixel(x2[t2][spoor-1],y2[t2][spoor-1],0);
449	for(t3=spoor-1;t3>0;t3--)
450	{ x2[t2][t3]=x2[t2][t3-1]; y2[t2][t3]=y2[t2][t3-1]; }
451	}
452	}
453	}
454	}
455	putchar(13); printf("Klaar");
456	fclose(bestand);
457	getch();
458	closegraph();
459	}
460
461	void main(void)
462	{ // Beginwaarden zetten.
463	stap=250; deel=3; r_o=100; r_n=.0001; t_frag=1; grens=0; w_g=500; spoor=0;
464	midd=0; spoor=0; modus=0;
465	clrscr(); textcolor(10);
466
467	// Grafische modus bepalen.
468	detectgraph(&t1, &t2);
469	initgraph(&t1, &t2, "..\\bgi");
470	x_max=getmaxx(); y_max=getmaxy();
471	closegraph();
472
473	// Test of standaard bestand bestaat.
474	strcpy(b_naam, "bestand.xyz");
475	b_test=0;
476	varbestand();
477
478	// Begin programma-lus.
479	prog=1;
480	do
481	{ menuopbeeld();
482	toets=0;
483	menuvraag();
484	// [b]estandsnaam.
485	if(toets==98) varbestand();
486	// [R]eken.
487	if(toets==82)
488	{ if(b_test==1)
489	{ printf("Bestand %s overschrijven? [j/n] ", b_naam);
490	i_temp=getch();
491	putchar(13); printf(" ");
492	putchar(13);
493	if(i_temp==106) b_test=0;
494	}
495	if(b_test==0)
496	{ willekeur();
497	if(grens>0\|\|t_frag!=1) rekenmetopties(); else reken();
498	}
499	}
500	if(toets==69)
501	{ if(b_test==1)
502	{ printf("Bestand %s overschrijven? [j/n] ", b_naam);
503	i_temp=getch();
504	putchar(13); printf(" ");
505	putchar(13);
506	if(i_temp==106) b_test=0;
507	}
508	if(b_test==0)
509	{ willekeur();
510	rekenenteken();
511	}
512	}
513	// [T]eken.
514	if(toets==84) teken();
515	if(toets==65) { willekeur(); geendisk(); }
516	if(toets==81) theorie();
517	if(toets==63) { printf("Bedacht en geschreven door G.J.Smit.");
518	getch(); }
519	if(toets==83) prog=0;
520	} while(prog>0);
521	}