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 "stdio.h"
6	#include "stdlib.h"
7	#include "conio.h"
8	#include "string.h"
9	#include "float.h"
10	#include "math.h"
11	#include "graphics.h"
12	#include "svga256.h"
13
14	FILE *bestand; // Pointer voor geopend bestand.
15	char b_naam[12]; // Naam van actief bestand.
16	char b_test; // Controle voor bestaan bestand.
17	char toets; // Variabele voor ingedrukte toets.
18	int t1,t2,t3,t4; // Tellers voor lussen.
19	int stap,dim,deel; // Aantal stappen, dimensies en deeltjes.
20	int spoor; // Lengte afbeelding in tijd per deeltje.
21	int prog; // Programma einde.
22	int i_temp; // Tijdelijk opslag integer.
23	int midd; // Middelpunt in tekening aan/uit.
24	int modus; // Kleur per deel/diepte.
25	float w_g, w_x, w_y; // Windowgrootte, x en y co rdinaatgrootte.
26	float x_max, y_max; // Aantal pixels op beeldscherm.
27	float t_frag, grens; // Tijdfragmentatie en grenswaarde ruimte.
28	float r_o, r_n; // Bereik willekeurige beginco rdinaten.
29	float fzx, fzy, fzz; // Zwaartekracht per as.
30	float g_temp; // Grenswaarde wisseling.
31	float f_temp; // Tijdelijk opslag float.
32	float midx, midy; // Middelpunt berekening-variabelen.
33	float diepte; // Kleur-diepte variabele.
34	float huge x3[1851][4]; // Maximaal 250 x3d-co rdinaten.
35	float huge y3[1851][4]; // Maximaal 250 y3d-co rdinaten.
36	float huge z3[1851][4]; // Maximaal 250 z3d-co rdinaten.
37	float huge x2[1851][30]; // Maximaal 30 x2d-co rdinaten per deeltje.
38	float huge y2[1851][30]; // Maximaal 30 y2d-co rdinaten per deeltje.
39
40	int huge DetectSvga256(){ int Vid; Vid=4; return Vid; }
41
42	void theorie(void) // Rekenkundig variabele verhoudingen.
43	{ t1=0; t2=2639;
44	installuserdriver("Svga256",DetectSvga256);
45	initgraph(&t1,&t2,"");
46	setcolor(7);
47	for(t1=0; t1<20; t1++)
48	{ line(x_max/2+200-t110, y_max/2, x_max/2, y_max/2+t110);
49	line(x_max/2-t110, y_max/2, x_max/2, y_max/2+200-t110);
50	line(x_max/2-200+t110, y_max/2, x_max/2, y_max/2-t110);
51	line(x_max/2+t110, y_max/2, x_max/2, y_max/2-200+t110);
52	}
53	getch();
54	closegraph();
55	}
56
57	void varbestand(void) // Variabele waarden bestand inlezen.
58	{ bestand=fopen(b_naam,"r");
59	if(bestand==NULL) b_test=0;
60	else
61	{ fscanf(bestand, "%d%d%f%f%f%f", &stap, &deel, &r_o, &r_n, &t_frag, &grens);
62	if(grens!=0) w_g=1.5*grens;
63	b_test=1;
64	}
65	fclose(bestand);
66	}
67
68	void menuopbeeld(void)
69	{ clrscr();
70	textcolor(10);
71	printf("[b]estandsnaam ");
72	if(b_test==0) printf("-"); else printf("+");
73	printf(" : %s\n\n", b_naam);
74	printf("[c]o rdinaten\n");
75	printf("[w]illekeur : %f\n", r_o);
76	printf("[r]ichting : %f\n\n", r_n);
77	printf("[t]ijdfragmentatie : %f\n", t_frag);
78	printf("[g]rens : %f\n\n", grens);
79	printf("[s]tappen : %d\n", stap);
80	printf("[d]eel : %d\n\n", deel);
81	printf("[v]enster : %f\n", w_g);
82	printf("[p]rojectie : %d\n", spoor);
83	printf("M goedmaken voor 3d: ");
84	//printf("[m]iddelpunt : ");
85	if(midd==0) printf("uit\n"); else printf("aan\n");
86	printf("[k]leurmodus : ");
87	if(modus==0) printf("deel\n\n\n"); else printf("diepte\n\n\n");
88	printf("[R]ekenen [E]n [T]ekenen [S]toppen\n\n");
89	}
90
91	void menuvraag(void)
92	{ toets=getch();
93	if(toets==98) { printf("Nieuwe bestandsnaam? ");
94	scanf("%s", &b_naam); }
95	if(toets==99) { printf("Invoer co rdinaten, nog programmeren...");
96	getch(); }
97	if(toets==119) { f_temp=r_o; printf("Maximale willekeur? ");
98	scanf("%f", &r_o);
99	if(r_o<0\|\|r_o==0\|\|r_o>30000) r_o=f_temp; }
100	if(toets==114) { f_temp=r_n; printf("Maximale richting? ");
101	scanf("%f", &r_n);
102	if(r_n<0\|\|r_o==0\|\|r_o>2500) r_o=f_temp; }
103	if(toets==116) { f_temp=t_frag; printf("Nieuwe tijdfragmentatie? ");
104	scanf("%f", &t_frag);
105	if(t_frag<0\|\|t_frag==0\|\|t_frag>1) t_frag=f_temp; }
106	if(toets==103) { f_temp=grens; printf("Grens van ruimte? ");
107	scanf("%f", &grens);
108	if(grens<0\|\|grens>32500) grens=f_temp; }
109	if(toets==115) { i_temp=stap; printf("Aantal stappen? ");
110	scanf("%d", &stap);
111	if(stap<1\|\|stap>32500) stap=i_temp; }
112	if(toets==100) { i_temp=deel; printf("Aantal deeltjes? ");
113	scanf("%d", &deel);
114	if(deel<2\|\|deel>1850) deel=i_temp; }
115	if(toets==118) { f_temp=w_g; printf("Venstergrootte? ");
116	scanf("%f", &w_g);
117	if(w_g<0\|\|w_g==0\|\|w_g>32500) w_g=f_temp; }
118	if(toets==112) { i_temp=spoor; printf("Aantal fragmenten? ");
119	scanf("%d", &spoor);
120	if(spoor<0\|\|spoor>30) spoor=i_temp; }
121	if(toets==109) { if(midd==0) midd=1; else midd=0; }
122	if(toets==107) { if(modus==0) modus=1; else modus=0; }
123	}
124
125	void willekeur(void)
126	{ for(t1=0;t1
127	{ x3[t1][0]=2(random(32767)r_o/32767)-r_o;
128	y3[t1][0]=2(random(32767)r_o/32767)-r_o;
129	z3[t1][0]=2(random(32767)r_o/32767)-r_o;
130	x3[t1][1]=x3[t1][0]+2(random(32767)r_n/32767)-r_n;
131	y3[t1][1]=y3[t1][0]+2(random(32767)r_n/32767)-r_n;
132	z3[t1][1]=z3[t1][0]+2(random(32767)r_n/32767)-r_n;
133	}
134	}
135
136	void reken(void) // Kaal [R]ekenen, snelste routine.
137	{ // Bestand voor co rdinaten openen.
138	bestand=fopen(b_naam,"w");
139	fprintf(bestand, "%d %d %f %f %f %f", stap, deel, r_o, r_n, t_frag, grens);
140	for(t1=0;t1
141	fprintf(bestand, " %f %f %f", x3[t1][1], y3[t1][1], z3[t1][1]);
142
143	// Co rdinaten berekenen, schrijven naar disk en naar tekst-beeldscherm.
144	for(t1=0;t1
145	{ for(t2=0;t2
146	{ x3[t2][3]=0;
147	y3[t2][3]=0;
148	z3[t2][3]=0;
149	}
150	for(t2=0;t2
151	{ x3[t2][2]=x3[t2][1]-x3[t2][0];
152	y3[t2][2]=y3[t2][1]-y3[t2][0];
153	z3[t2][2]=z3[t2][1]-z3[t2][0];
154	for(t3=t2;t3
155	{ fzx=x3[t3][1]-x3[t2][1];
156	fzy=y3[t3][1]-y3[t2][1];
157	fzz=z3[t3][1]-z3[t2][1];
158	if(fzx!=0) { fzx=1/fzx; x3[t2][3]=x3[t2][3]+fzx;
159	x3[t3][3]=x3[t3][3]-fzx; }
160	if(fzy!=0) { fzy=1/fzy; y3[t2][3]=y3[t2][3]+fzy;
161	y3[t3][3]=y3[t3][3]-fzy; }
162	if(fzz!=0) { fzz=1/fzz; z3[t2][3]=z3[t2][3]+fzz;
163	z3[t3][3]=z3[t3][3]-fzz; }
164	}
165	x3[t2][0]=x3[t2][1];
166	y3[t2][0]=y3[t2][1];
167	z3[t2][0]=z3[t2][1];
168	x3[t2][1]=x3[t2][0]+x3[t2][2]+x3[t2][3];
169	y3[t2][1]=y3[t2][0]+y3[t2][2]+y3[t2][3];
170	z3[t2][1]=z3[t2][0]+z3[t2][2]+z3[t2][3];
171	}
172	for(t2=0;t2
173	fprintf(bestand, " %f %f %f", x3[t2][1], y3[t2][1], z3[t2][1]);
174	putchar(13); printf("%d",t1+1);
175	}
176	fclose(bestand);
177	b_test=1;
178	}
179
180	void rekenmetopties(void) // [R]ekenen met grens en/of t_frag aan.
181	{ // Bestand voor co rdinaten openen.
182	bestand=fopen(b_naam,"w");
183	fprintf(bestand, "%d %d %f %f %f %f", stap, deel, r_o, r_n, t_frag, grens);
184	for(t1=0;t1
185	fprintf(bestand, " %f %f %f", x3[t1][1], y3[t1][1], z3[t1][1]);
186
187	// Co rdinaten berekenen, schrijven naar disk en naar tekst-beeldscherm.
188	for(t1=0;t1
189	{ for(t2=0;t2
190	{ x3[t2][3]=0;
191	y3[t2][3]=0;
192	z3[t2][3]=0;
193	}
194	for(t2=0;t2
195	{ x3[t2][2]=x3[t2][1]-x3[t2][0];
196	y3[t2][2]=y3[t2][1]-y3[t2][0];
197	z3[t2][2]=z3[t2][1]-z3[t2][0];
198	for(t3=t2;t3
199	{ fzx=x3[t3][1]-x3[t2][1];
200	fzy=y3[t3][1]-y3[t2][1];
201	fzz=z3[t3][1]-z3[t2][1];
202	if(fzx!=0) { fzx=1/fzx; x3[t2][3]=x3[t2][3]+fzx;
203	x3[t3][3]=x3[t3][3]-fzx; }
204	if(fzy!=0) { fzy=1/fzy; y3[t2][3]=y3[t2][3]+fzy;
205	y3[t3][3]=y3[t3][3]-fzy; }
206	if(fzz!=0) { fzz=1/fzz; z3[t2][3]=z3[t2][3]+fzz;
207	z3[t3][3]=z3[t3][3]-fzz; }
208	}
209	// Bewerk co rdinaten als t_frag ongelijk aan 1.
210	if(t_frag!=1)
211	{ x3[t2][2]=x3[t2][2]t_frag; x3[t2][3]=x3[t2][3]t_frag;
212	y3[t2][2]=y3[t2][2]t_frag; y3[t2][3]=y3[t2][3]t_frag;
213	z3[t2][2]=z3[t2][2]t_frag; z3[t2][3]=z3[t2][3]t_frag;
214	}
215	// Bepaal de nieuwe co rdinaten.
216	x3[t2][0]=x3[t2][1];
217	y3[t2][0]=y3[t2][1];
218	z3[t2][0]=z3[t2][1];
219	x3[t2][1]=x3[t2][0]+x3[t2][2]+x3[t2][3];
220	y3[t2][1]=y3[t2][0]+y3[t2][2]+y3[t2][3];
221	z3[t2][1]=z3[t2][0]+z3[t2][2]+z3[t2][3];
222	// Test grensoverschrijding.
223	if(grens>0)
224	{ if(x3[t2][1]<-grens\|\|x3[t2][1]>grens)
225	{ g_temp=x3[t2][1]; x3[t2][1]=-x3[t2][0]; x3[t2][0]=-g_temp; }
226	if(y3[t2][1]<-grens\|\|y3[t2][1]>grens)
227	{ g_temp=y3[t2][1]; y3[t2][1]=-y3[t2][0]; y3[t2][0]=-g_temp; }
228	if(z3[t2][1]<-grens\|\|z3[t2][1]>grens)
229	{ g_temp=z3[t2][1]; z3[t2][1]=-z3[t2][0]; z3[t2][0]=-g_temp; }
230	}
231	}
232	for(t2=0;t2
233	fprintf(bestand, " %f %f %f", x3[t2][1], y3[t2][1], z3[t2][1]);
234	putchar(13); printf("%d",t1+1);
235	}
236	fclose(bestand);
237	b_test=1;
238	}
239
240	void rekenenteken(void) // [E]n.
241	{ t1=0; t2=2639;
242	installuserdriver("Svga256",DetectSvga256);
243	initgraph(&t1,&t2,"");
244	w_x=(x_max+1)/(w_g2); w_y=(y_max+1)/(w_g2);
245	printf(" \|%d\|%d\|%f\|%f\|%f\|%f\|%f\|%d\|%s",
246	stap, deel, r_o, r_n, t_frag, grens, w_g, spoor, b_naam);
247	gotoxy(0,0);
248	midd=0; spoor=0; modus=0;
249
250	// Bestand voor co rdinaten openen.
251	bestand=fopen(b_naam,"w");
252	fprintf(bestand, "%d %d %f %f %f %f", stap, deel, r_o, r_n, t_frag, grens);
253	for(t1=0;t1
254	fprintf(bestand, " %f %f %f", x3[t1][1], y3[t1][1], z3[t1][1]);
255
256	// Co rdinaten berekenen, schrijven naar disk en naar grafisch beeldscherm.
257	for(t1=0;t1
258	{ for(t2=0;t2
259	{ x3[t2][3]=0;
260	y3[t2][3]=0;
261	z3[t2][3]=0;
262	}
263	for(t2=0;t2
264	{ x3[t2][2]=x3[t2][1]-x3[t2][0];
265	y3[t2][2]=y3[t2][1]-y3[t2][0];
266	z3[t2][2]=z3[t2][1]-z3[t2][0];
267	for(t3=t2;t3
268	{ fzx=x3[t3][1]-x3[t2][1];
269	fzy=y3[t3][1]-y3[t2][1];
270	fzz=z3[t3][1]-z3[t2][1];
271	if(fzx!=0) { fzx=1/fzx; x3[t2][3]=x3[t2][3]+fzx;
272	x3[t3][3]=x3[t3][3]-fzx; }
273	if(fzy!=0) { fzy=1/fzy; y3[t2][3]=y3[t2][3]+fzy;
274	y3[t3][3]=y3[t3][3]-fzy; }
275	if(fzz!=0) { fzz=1/fzz; z3[t2][3]=z3[t2][3]+fzz;
276	z3[t3][3]=z3[t3][3]-fzz; }
277	}
278	// Bewerk co rdinaten als t_frag ongelijk aan 1.
279	if(t_frag!=1)
280	{ x3[t2][2]=x3[t2][2]t_frag; x3[t2][3]=x3[t2][3]t_frag;
281	y3[t2][2]=y3[t2][2]t_frag; y3[t2][3]=y3[t2][3]t_frag;
282	z3[t2][2]=z3[t2][2]t_frag; z3[t2][3]=z3[t2][3]t_frag;
283	}
284	// Bepaal de nieuwe co rdinaten.
285	x3[t2][0]=x3[t2][1];
286	y3[t2][0]=y3[t2][1];
287	z3[t2][0]=z3[t2][1];
288	x3[t2][1]=x3[t2][0]+x3[t2][2]+x3[t2][3];
289	y3[t2][1]=y3[t2][0]+y3[t2][2]+y3[t2][3];
290	z3[t2][1]=z3[t2][0]+z3[t2][2]+z3[t2][3];
291	// Test grensoverschrijding.
292	if(grens>0)
293	{ if(x3[t2][1]<-grens\|\|x3[t2][1]>grens)
294	{ g_temp=x3[t2][1]; x3[t2][1]=-x3[t2][0]; x3[t2][0]=-g_temp; }
295	if(y3[t2][1]<-grens\|\|y3[t2][1]>grens)
296	{ g_temp=y3[t2][1]; y3[t2][1]=-y3[t2][0]; y3[t2][0]=-g_temp; }
297	if(z3[t2][1]<-grens\|\|z3[t2][1]>grens)
298	{ g_temp=z3[t2][1]; z3[t2][1]=-z3[t2][0]; z3[t2][0]=-g_temp; }
299	}
300	}
301	for(t2=0;t2
302	fprintf(bestand, " %f %f %f", x3[t2][1], y3[t2][1], z3[t2][1]);
303	for(t2=0;t2
304	{ x2[t2][0]=y3[t2][1]-x3[t2][1];
305	y2[t2][0]=-z3[t2][1]+x3[t2][1]/2;
306	x2[t2][0]=x_max/2-w_x*x2[t2][0];
307	y2[t2][0]=y_max/2-w_y*y2[t2][0];
308	putpixel(x2[t2][0],y2[t2][0],2+t2);
309	}
310	putchar(13); printf("%d",t1+1);
311	}
312	putchar(13); printf("Klaar");
313	fclose(bestand);
314	b_test=1;
315	getch();
316	closegraph();
317	}
318
319	void geendisk(void) // [A]lleen rekenen en tekenen.
320	{ t1=0; t2=2639;
321	installuserdriver("Svga256",DetectSvga256);
322	initgraph(&t1,&t2,"");
323	w_x=(x_max+1)/(w_g2); w_y=(y_max+1)/(w_g2);
324	if(modus!=0) diepte=255/(w_g*2);
325
326	printf(" \|%d\|%d\|%f\|%f\|%f\|%f\|%f\|%d\|XXXXXX",
327	stap, deel, r_o, r_n, t_frag, grens, w_g, spoor);
328	gotoxy(0,0);
329
330	// Co rdinaten berekenen, schrijven naar grafisch beeldscherm.
331	for(t1=0;t1
332	{ for(t2=0;t2
333	{ x3[t2][3]=0;
334	y3[t2][3]=0;
335	z3[t2][3]=0;
336	}
337	putchar(13);printf("%d", t1);
338	if(midd>0) { midx=0; midy=0; }
339	for(t2=0;t2
340	{ x3[t2][2]=x3[t2][1]-x3[t2][0];
341	y3[t2][2]=y3[t2][1]-y3[t2][0];
342	z3[t2][2]=z3[t2][1]-z3[t2][0];
343	for(t3=t2;t3
344	{ fzx=x3[t3][1]-x3[t2][1];
345	fzy=y3[t3][1]-y3[t2][1];
346	fzz=z3[t3][1]-z3[t2][1];
347	if(fzx!=0) { fzx=1/fzx; x3[t2][3]=x3[t2][3]+fzx;
348	x3[t3][3]=x3[t3][3]-fzx; }
349	if(fzy!=0) { fzy=1/fzy; y3[t2][3]=y3[t2][3]+fzy;
350	y3[t3][3]=y3[t3][3]-fzy; }
351	if(fzz!=0) { fzz=1/fzz; z3[t2][3]=z3[t2][3]+fzz;
352	z3[t3][3]=z3[t3][3]-fzz; }
353	}
354	// Bewerk co rdinaten als t_frag ongelijk aan 1.
355	if(t_frag!=1)
356	{ x3[t2][2]=x3[t2][2]t_frag; x3[t2][3]=x3[t2][3]t_frag;
357	y3[t2][2]=y3[t2][2]t_frag; y3[t2][3]=y3[t2][3]t_frag;
358	z3[t2][2]=z3[t2][2]t_frag; z3[t2][3]=z3[t2][3]t_frag;
359	}
360	// Bepaal de nieuwe co rdinaten.
361	x3[t2][0]=x3[t2][1];
362	y3[t2][0]=y3[t2][1];
363	z3[t2][0]=z3[t2][1];
364	x3[t2][1]=x3[t2][0]+x3[t2][2]+x3[t2][3];
365	y3[t2][1]=y3[t2][0]+y3[t2][2]+y3[t2][3];
366	z3[t2][1]=z3[t2][0]+z3[t2][2]+z3[t2][3];
367	// Test grensoverschrijding.
368	if(grens>0)
369	{ if(x3[t2][1]<-grens\|\|x3[t2][1]>grens)
370	{ g_temp=x3[t2][1]; x3[t2][1]=-x3[t2][0]; x3[t2][0]=-g_temp; }
371	if(y3[t2][1]<-grens\|\|y3[t2][1]>grens)
372	{ g_temp=y3[t2][1]; y3[t2][1]=-y3[t2][0]; y3[t2][0]=-g_temp; }
373	if(z3[t2][1]<-grens\|\|z3[t2][1]>grens)
374	{ g_temp=z3[t2][1]; z3[t2][1]=-z3[t2][0]; z3[t2][0]=-g_temp; }
375	}
376	}
377	for(t2=0;t2
378	{ x2[t2][0]=y3[t2][1]-x3[t2][1];
379	y2[t2][0]=-z3[t2][1]+x3[t2][1]/2;
380	if(midd>0)
381	{ midx=midx+x2[t2][0];
382	midy=midy+y2[t2][0];
383	}
384	}
385	if(midd>0) { midx=midx/deel; midy=midy/deel; }
386	for(t2=0;t2
387	{ if(midd>0)
388	{ x2[t2][0]=x_max/2+midx-w_x*x2[t2][0];
389	y2[t2][0]=y_max/2+midy-w_y*y2[t2][0];
390	}
391	else
392	{ x2[t2][0]=x_max/2-w_x*x2[t2][0];
393	y2[t2][0]=y_max/2-w_y*y2[t2][0];
394	}
395	if(modus==0) putpixel(x2[t2][0],y2[t2][0],2+t2);
396	else putpixel(x2[t2][0],y2[t2][0],1+(x3[t2][1]+w_g)*diepte);
397	if(spoor>0)
398	{ if(t1
399	{ x2[t2][spoor-1-t1]=x2[t2][0]; y2[t2][spoor-1-t1]=y2[t2][0]; }
400	else
401	{ putpixel(x2[t2][spoor-1],y2[t2][spoor-1],0);
402	for(t3=spoor-1;t3>0;t3--)
403	{ x2[t2][t3]=x2[t2][t3-1]; y2[t2][t3]=y2[t2][t3-1]; }
404	}
405	}
406	}
407	putchar(13); printf("%d",t1+1);
408	}
409	putchar(13); printf("Klaar");
410	getch();
411	closegraph();
412	}
413
414	void teken(void)
415	{ t1=0; t2=2639;
416	installuserdriver("Svga256",DetectSvga256);
417	initgraph(&t1,&t2,"");
418
419	// Berekenen hoeveelheid pixels per nheid.
420	w_x=(x_max+1)/(w_g2); w_y=(y_max+1)/(w_g2);
421
422	bestand=fopen(b_naam,"r");
423	fscanf(bestand, "%d%d%f%f%f%f", &stap, &deel, &r_o, &r_n, &t_frag, &grens);
424	printf(" \|%d\|%d\|%f\|%f\|%f\|%f\|%f\|%d\|%s",
425	stap, deel, r_o, r_n, t_frag, grens, w_g, spoor, b_naam);
426
427	if(modus!=0) diepte=255/(w_g*2);
428	for(t1=0;t1
429	{ putchar(13);printf("%d", t1);
430	if(midd>0) { midx=0; midy=0; }
431	for(t2=0;t2
432	fscanf(bestand, "%f%f%f", &x3[t2][1], &y3[t2][1], &z3[t2][1]);
433	for(t2=0;t2
434	{ x2[t2][0]=y3[t2][1]-x3[t2][1];
435	y2[t2][0]=-z3[t2][1]+x3[t2][1]/2;
436	if(midd>0)
437	{ midx=midx+x2[t2][0];
438	midy=midy+y2[t2][0];
439	}
440	}
441	if(midd>0) { midx=midx/deel; midy=midy/deel; }
442	for(t2=0;t2
443	{ if(midd>0)
444	{ x2[t2][0]=x_max/2+midx-w_x*x2[t2][0];
445	y2[t2][0]=y_max/2+midy-w_y*y2[t2][0];
446	}
447	else
448	{ x2[t2][0]=x_max/2-w_x*x2[t2][0];
449	y2[t2][0]=y_max/2-w_y*y2[t2][0];
450	}
451	if(modus==0) putpixel(x2[t2][0],y2[t2][0],2+t2);
452	else putpixel(x2[t2][0],y2[t2][0],1+(x3[t2][1]+w_g)*diepte);
453	if(spoor>0)
454	{ if(t1
455	{ x2[t2][spoor-1-t1]=x2[t2][0]; y2[t2][spoor-1-t1]=y2[t2][0]; }
456	else
457	{ putpixel(x2[t2][spoor-1],y2[t2][spoor-1],0);
458	for(t3=spoor-1;t3>0;t3--)
459	{ x2[t2][t3]=x2[t2][t3-1]; y2[t2][t3]=y2[t2][t3-1]; }
460	}
461	}
462	}
463	}
464	putchar(13); printf("Klaar");
465	fclose(bestand);
466	getch();
467	closegraph();
468	}
469
470	void main(void)
471	{ // Beginwaarden zetten.
472	stap=250; deel=3; r_o=100; r_n=.0001; t_frag=1; grens=0; w_g=500; spoor=0;
473	midd=0; spoor=0; modus=0;
474	clrscr(); textcolor(10);
475
476	// Grafische modus bepalen.
477	t1=0; t2=2639;
478	installuserdriver("Svga256",DetectSvga256);
479	initgraph(&t1,&t2,"");
480	x_max=getmaxx(); y_max=getmaxy();
481	closegraph();
482
483	// Test of standaard bestand bestaat.
484	strcpy(b_naam, "bestand.xyz");
485	b_test=0;
486	varbestand();
487
488	// Begin programma-lus.
489	prog=1;
490	do
491	{ menuopbeeld();
492	toets=0;
493	menuvraag();
494	// [b]estandsnaam.
495	if(toets==98) varbestand();
496	// [R]eken.
497	if(toets==82)
498	{ if(b_test==1)
499	{ printf("Bestand %s overschrijven? [j/n] ", b_naam);
500	i_temp=getch();
501	putchar(13); printf(" ");
502	putchar(13);
503	if(i_temp==106) b_test=0;
504	}
505	if(b_test==0)
506	{ willekeur();
507	if(grens>0\|\|t_frag!=1) rekenmetopties(); else reken();
508	}
509	}
510	if(toets==69)
511	{ if(b_test==1)
512	{ printf("Bestand %s overschrijven? [j/n] ", b_naam);
513	i_temp=getch();
514	putchar(13); printf(" ");
515	putchar(13);
516	if(i_temp==106) b_test=0;
517	}
518	if(b_test==0)
519	{ willekeur();
520	rekenenteken();
521	}
522	}
523	// [T]eken.
524	if(toets==84) teken();
525	if(toets==65) { willekeur(); geendisk(); }
526	if(toets==81) theorie();
527	if(toets==63) { printf("Bedacht en geschreven door G.J.Smit.");
528	getch(); }
529	if(toets==83) prog=0;
530	} while(prog>0);
531	}
532