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	demo.design 3D programming FAQ

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ÎÑÂÅÙÅÍÈÅ<br>5.2. Ðàñ÷åò íîðìàëè ê îáúåêòó

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<p>Âî âñåõ ôîðìóëàõ äëÿ îñâåùåííîñòè ó íàñ òàê èëè èíà÷å áóäåò ôèãóðèðîâàòü
âåêòîð N - íîðìàëü ê îáúåêòó â òî÷êå P. Ñðàçó âîçíèêàåò âîïðîñ, à êàê æå
ýòîò âåêòîð ñ÷èòàòü.

<p>Îáû÷íî ïðèäåðæèâàþòñÿ òàêîé ëîãèêè. Ìîäåëü ó íàñ ñîñòîèò èç ïëîñêèõ ãðàíåé,
íî ýòà ñåòêà ïëîñêèõ ãðàíåé ïðèáëèæàåò êàêîé-òî èñêðèâëåííûé îáúåêò. Íîðìàëü
ê ýòîìó èñêðèâëåííîìó îáúåêòó ìåíÿåòñÿ â êàæäîé òî÷êå, à äëÿ ïëîñêèõ ãðàíåé
îíà ïîñòîÿííà äëÿ âñåõ òî÷åê ãðàíè, è ðåçêî ìåíÿåòñÿ ïðè ïåðåõîäå íà äðóãóþ
ãðàíü. Ïîýòîìó íîðìàëü ê îáúåêòó îáû÷íî ïðèáëèæàþò ñëåäóþùèì îáðàçîì: ñ÷èòàþò
íîðìàëè â âåðøèíàõ, à íîðìàëü â êàêîé-òî òî÷êå ãðàíè ëèíåéíî èíòåðïîëèðóþò
ìåæäó âåðøèíàìè; òî åñòü ëèíåéíî èíòåðïîëèðóþò ïî ãðàíè âñå òðè êîîðäèíàòû
íîðìàëè.

<p>Íîðìàëü â âåðøèíå ðàññ÷èòûâàþòñÿ êàê ñóììà ïðèâåäåííûõ ê äëèíå 1 íîðìàëåé êî
âñåì ãðàíÿì, ê êîòîðûì ïðèíàäëåæèò ýòà âåðøèíà. Òî åñòü. Ñíà÷àëà ñ÷èòàåì
íîðìàëè êî âñåì ãðàíÿì è ïðèâîäèì èõ ê äëèíå 1. Äàëåå, äëÿ êàæäîé âåðøèíû
íàäî ïåðåáðàòü âñå ãðàíè, è åñëè î÷åðåäíàÿ ãðàíü ñîäåðæèò ýòó âåðøèíó, òî
ê íîðìàëè â âåðøèíå ïðèáàâëÿåòñÿ íîðìàëü ê ýòîé ãðàíè. Ïåðâîíà÷àëüíî âñå
íîðìàëè ê âåðøèíàì ïîëàãàþòñÿ ðàâíûìè íóëþ. Äëÿ áîëüøèõ ìîäåëåé ýòîò ïðîöåññ
ìîæåò áûòü äîâîëüíî äîëãèì, íî äîñòàòî÷íî ïðîâåñòè åãî çàðàíåå îäèí ðàç è
ñîõðàíèòü âñå ïîñ÷èòàííûå íîðìàëè ê âåðøèíàì.

<p>Äëÿ âÿùåé ïîíÿòíîñòè ïðèâåäó êóñîê êîäà:

<pre class=source>
// ...
for (i = 0; i < numberOfVertics; i++) {
  vertexNormal[i].x = 0;
  vertexNormal[i].y = 0;
  vertexNormal[i].z = 0;
}
for (i = 0; i < numberOfVertics; i++) {
  for (j = 0; j < numberOfFaces; j++) {
    if (face[j].vertex0 == i ||
        face[j].vertex1 == i ||
        face[j].vertex2 == i)
    {
      vertexNormal[i].x += faceNormal[j].x;
      vertexNormal[i].y += faceNormal[j].y;
      vertexNormal[i].z += faceNormal[j].z;
    }
  }
}
// ...
</pre>

<p>Íî ýòî ìåòîä äàæå ñëèøêîì ëîáîâîé, è ïîýòîìó ìåäëåííûé. Ìîæíî ñäåëàòü âñå
ïðîùå è áûñòðåå: ïåðåáèðàåì âñå ãðàíè, è ê íîðìàëÿì âñåõ ïðèíàäëåæàùèõ ãðàíè
âåðøèí äîáàâëÿåì íîðìàëü ãðàíè. Ïîñëå ýòîãî ïðèâîäèì âñå íîðìàëè ê äëèíå 1,
ïðè÷åì ýòà ôàçà äàæå íå îáÿçàòåëüíà, à ëèøü óäîáíà äëÿ äàëüíåéøèõ ðàñ÷åòîâ.
Ñîîòâåòñòâóþùèé êóñî÷åê êîäà:

<pre class=source>
// ...
for (i = 0; i < numberOfVertics; i++) {
  vertexNormal[i].x = 0;
  vertexNormal[i].y = 0;
  vertexNormal[i].z = 0;
}
for (i = 0; i < numberOfFaces; i++) {
  vertexNormal[face[i].vertex0].x += faceNormal[j].x;
  vertexNormal[face[i].vertex1].y += faceNormal[j].y;
  vertexNormal[face[i].vertex2].z += faceNormal[j].z;
}
// ...
</pre>

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