Question

我想将一个对象（立方体）乘以一定数量，在这种情况下，我们说25，我确实有一个立方体的代码，它可以工作，但我无法计算如何制作更多。我是GLUT的新人。

const
  base1     =
 '0x00be5416af9696937b7234421f7256f78dba8001c80a5fdecdb4ed761f2b7f955946ec9203'+
 '99f23ce9627f66286239d3f20e7a46df185946c6c8482e227b9ce172dd518202381706ed0f91'+
 'b53c5436f233dec27e8cb46c4478f0398d2c254021a7c21596b30f77e9886e2fd2a081cadd3f'+
 'af83c86bfdd6e9daad12559f8d2747';
  exponent1 =
 '0x6f1e6ab386677cdc86a18f24f42073b328847724fbbd293eee9cdec29ac4dfe953a4256d7e'+
 '6b9abee426db3b4ddc367a9fcf68ff168a7000d3a7fa8b9d9064ef4f271865045925660fab62'+
 '0fad0aeb58f946e33bdff6968f4c29ac62bd08cf53cb8be2116f2c339465a64fd02517f2bafc'+
 'a72c9f3ca5bbf96b24c1345eb936d1';
  modulus1  =
 '0xb4d92132b03210f62e52129ae31ef25e03c2dd734a7235efd36bad80c28885f3a9ee1ab626'+
 'c30072bb3fd9906bf89a259ffd9d5fd75f87a30d75178b9579b257b5dca13ca7546866ad9f2d'+
 'b0072d59335fb128b7295412dd5c43df2c4f2d2f9c1d59d2bb444e6dac1d9cef27190a97aae7'+
 '030c5c004c5aea3cf99afe89b86d6d';

function MontMult(X, Y, N: BigInteger): BigInteger;
var
  I: Integer;
begin
  Result:= 0;
  for I:= 0 to 1023 do begin
    if not X.IsEven then Result:= Result + Y;
    if not Result.IsEven then Result:= Result + N;
    Result:= Result shr 1;
    X:= X shr 1;
  end;
  if Result >= N then Result:= Result - N;
end;

function ModExp(B, E, N: BigInteger): BigInteger;
var
  R, MontB: BigInteger;
  I: Integer;

begin
  R:= BigInteger.PowerOfTwo(1024) mod N;
  MontB:= (B * R) mod N;
  for I:= 1023 downto 0 do begin
    R:= MontMult(R, R, N);
    if not (E shr I).IsEven then
      R:= MontMult(MontB, R, N);
  end;
  Result:= MontMult(R, 1, N);
end;

procedure TestMontMult;
var
  Base, Expo, Modulus: BigInteger;
  MontBase, MontExpo: BigInteger;
  X, Y, R: BigInteger;
  Mont: TMont;

begin
// convert to BigInteger
  Base:= BigInteger.Parse(base1);
  Expo:= BigInteger.Parse(exponent1);
  Modulus:= BigInteger.Parse(modulus1);

  R:= BigInteger.PowerOfTwo(1024) mod Modulus;
// Convert into Montgomery form
  MontBase:= (Base * R) mod Modulus;
  MontExpo:= (Expo * R) mod Modulus;
  Writeln;

// MontMult test, all 3 versions output
//  '0x146005377258684F3FFD8D9A70D723BDD3A2E3A160E11B7AD35A7106D4D903AB9D14A9201'+
//  'D0907CE2FC2E04A69656C38CE64AA0BADF2376AEFB19D8732CE2B3650466E31BB78CF24F4E3'+
//  '774A78575738B668DA0E40C8DDDA972CE101E0CADC5D4CCFF6EF2E4E97AF02F34E3AB7258A7'+
//  '323E472FC051825FFC72ADC53B0DAF3C4';
  Writeln('Using MontMult');
  Writeln(MontMult(MontMult(MontBase, MontExpo, Modulus), 1, Modulus).ToHexString);
// same using TMont instance
  Writeln('Using TMont.Multiply');
  Mont:= TMont.GetInstance(Modulus);
  Writeln(Mont.Reduce(Mont.Multiply(MontBase, MontExpo)).ToHexString);
  Writeln('Using TMont.ModMul');
  Writeln(Mont.ModMul(Base,Expo).ToHexString);

// ModExp test, all 3 versions output 29
  Writeln('Using ModExp');
  Writeln(ModExp(Base, Expo, Modulus).ToString);
  Writeln('Using BigInteger.ModPow');
  Writeln(BigInteger.ModPow(Base, Expo, Modulus).ToString);
  Writeln('Using TMont.ModPow');
  Writeln(Mont.ModPow(Base, Expo).ToString);
end;

如果有更详细的指南，如果您分享，我会感激不尽。

Answer 1

每次拨打glutSolidCube()时，都会绘制一个多维数据集。如果您希望显示多个多维数据集，则需要在display()的实现中多次调用该函数。

（确保在每次调用之间更改模型矩阵！否则，立方体将最终位于同一位置。）

GLUT中有多个对象

1 个答案: