如何在 iOS 设备中动态显示数学方程？答案

【问题标题】：How to display mathematical equations dynamically in iOS devices?如何在 iOS 设备中动态显示数学方程？
【发布时间】：2012-01-14 03:13:33
【问题描述】：

我使用 Quartz2D 为 iPod/iPhone 绘制数学方程，下面是示例代码。

问题：在我的应用程序中，我必须动态显示许多这些方程。我是否需要从 plist（或其他存储）中动态读取 data to draw 及其 x / y 坐标，然后绘制方程？ em> 现在我只是对数据和 x / y 坐标进行硬编码（如下面的示例代码所示 - ）。

- (void)drawRect:(CGRect)rect
{
// Left hand side Starts --
float xaxis = 3.0f;

// Before bracket
NSString *textString = @"L";
[textString drawAtPoint:CGPointMake(xaxis, 50.) withFont:[UIFont fontWithName:@"Helvetica-Oblique" size:20]];

// Opening bracket
xaxis += 12.0f;
textString = @"(";
[textString drawAtPoint:CGPointMake(xaxis, 30.) withFont:[UIFont fontWithName:@"Helvetica" size:50]];

textString = @"N";
xaxis += 12.0f;
[textString drawAtPoint:CGPointMake(xaxis, 50.) withFont:[UIFont fontWithName:@"Helvetica-Oblique" size:20]];

// Numerator part
unichar oneChar[] = {0x2206};
xaxis += 31.0f;
textString = getTextString(oneChar, 1);
[textString drawAtPoint:CGPointMake(xaxis, 37.) withFont:[UIFont fontWithName:@"Helvetica" size:22]];

unichar twoChar[] = {0x03C9};
xaxis += 15.0f;
textString = getTextString(twoChar, 1);
[textString drawAtPoint:CGPointMake(xaxis, 38.) withFont:[UIFont fontWithName:@"Helvetica" size:20]];

xaxis += 15.0f;
textString = @"k";
[textString drawAtPoint:CGPointMake(xaxis, 48.) withFont:[UIFont fontWithName:@"Helvetica" size:12]];

// Line
CGContextRef myContext = UIGraphicsGetCurrentContext();    
CGContextSetLineWidth(myContext, 2);
CGContextSetStrokeColorWithColor(myContext, [UIColor blackColor].CGColor);    
CGContextMoveToPoint(myContext, 45, 65);
CGContextAddLineToPoint(myContext, 110, 65);
CGContextStrokePath(myContext);

// Denominator part
xaxis -= 40.0f;
unichar threeChar[] = {0x03C9};
textString = getTextString(threeChar, 1);
[textString drawAtPoint:CGPointMake(xaxis, 64.) withFont:[UIFont fontWithName:@"Helvetica" size:20]];

xaxis += 15.0f;
textString = @"res";
[textString drawAtPoint:CGPointMake(xaxis, 74.) withFont:[UIFont fontWithName:@"Helvetica" size:12]];

xaxis += 18.0f;
unichar fourChar[] = {0x0028};
textString = getTextString(fourChar, 1);
[textString drawAtPoint:CGPointMake(xaxis, 64.) withFont:[UIFont fontWithName:@"Helvetica" size:20]];

xaxis += 5.0f;
unichar fiveChar[] = {0x03B8};
textString = getTextString(fiveChar, 1);
[textString drawAtPoint:CGPointMake(xaxis, 64.) withFont:[UIFont fontWithName:@"Helvetica-Oblique" size:20]];

xaxis += 15.0f;
textString = @")";
[textString drawAtPoint:CGPointMake(xaxis, 64.) withFont:[UIFont fontWithName:@"Helvetica" size:20]];

// Closing bracket
xaxis += 8.0f;
textString = @")";
[textString drawAtPoint:CGPointMake(xaxis, 30.) withFont:[UIFont fontWithName:@"Helvetica" size:50]];

// Equal to sign
xaxis += 15.0f;
unichar sixChar[] = {0x003D};
textString = getTextString(sixChar, 1);
[textString drawAtPoint:CGPointMake(xaxis, 50.) withFont:[UIFont fontWithName:@"Helvetica" size:20]];

// Right hand side Starts --

// Numerator part
xaxis += 15.0f;
textString = @"sin";
[textString drawAtPoint:CGPointMake(xaxis, 42.) withFont:[UIFont fontWithName:@"Helvetica" size:17]];

xaxis += 20.0f;
textString = @"2";
[textString drawAtPoint:CGPointMake(xaxis, 38.) withFont:[UIFont fontWithName:@"Helvetica" size:12]];

// Inner opening bracket
xaxis += 10.0f;
textString = @"(";
[textString drawAtPoint:CGPointMake(xaxis, 37.) withFont:[UIFont fontWithName:@"Helvetica" size:22]];

xaxis += 8.0f;
textString = @"N";
[textString drawAtPoint:CGPointMake(xaxis, 38.) withFont:[UIFont fontWithName:@"Helvetica-Oblique" size:20]];

xaxis += 18.0f;
unichar sevenChar[] = {0x03C0};
textString = getTextString(sevenChar, 1);
[textString drawAtPoint:CGPointMake(xaxis, 40.) withFont:[UIFont fontWithName:@"Helvetica" size:17]];

xaxis += 12.0f;
unichar eightChar[] = {0x2206};
textString = getTextString(eightChar, 1);
[textString drawAtPoint:CGPointMake(xaxis, 36.) withFont:[UIFont fontWithName:@"Helvetica" size:21]];

xaxis += 15.0f;
unichar nineChar[] = {0x03C9};
textString = getTextString(nineChar, 1);
[textString drawAtPoint:CGPointMake(xaxis, 38.) withFont:[UIFont fontWithName:@"Helvetica" size:20]];

xaxis += 15.0f;
textString = @"k";
[textString drawAtPoint:CGPointMake(xaxis, 47.) withFont:[UIFont fontWithName:@"Helvetica" size:12]];

xaxis += 8.0f;
textString = @"/";
[textString drawAtPoint:CGPointMake(xaxis, 38.) withFont:[UIFont fontWithName:@"Helvetica" size:24]];

xaxis += 8.0f;
unichar tenChar[] = {0x03C9};
textString = getTextString(tenChar, 1);
[textString drawAtPoint:CGPointMake(xaxis, 38.) withFont:[UIFont fontWithName:@"Helvetica" size:20]];

xaxis += 15.0f;
textString = @"res";
[textString drawAtPoint:CGPointMake(xaxis, 48.) withFont:[UIFont fontWithName:@"Helvetica" size:12]];

xaxis += 18.0f;
textString = @"(";
[textString drawAtPoint:CGPointMake(xaxis, 38.) withFont:[UIFont fontWithName:@"Helvetica" size:20]];

xaxis += 5.0f;
unichar elevenChar[] = {0x03B8};
textString = getTextString(elevenChar, 1);
[textString drawAtPoint:CGPointMake(xaxis, 38.) withFont:[UIFont fontWithName:@"Helvetica-Oblique" size:20]];

xaxis += 12.0f;
textString = @")";
[textString drawAtPoint:CGPointMake(xaxis, 38.) withFont:[UIFont fontWithName:@"Helvetica" size:20]];

// Inner closing bracket
xaxis += 6.0f;
textString = @")";
[textString drawAtPoint:CGPointMake(xaxis, 37.) withFont:[UIFont fontWithName:@"Helvetica" size:22]];

// Line    
CGContextSetLineWidth(myContext, 2);
CGContextSetStrokeColorWithColor(myContext, [UIColor blackColor].CGColor);    
CGContextMoveToPoint(myContext, 138, 65);
CGContextAddLineToPoint(myContext, 318, 65);
CGContextStrokePath(myContext);

// Denominator part
xaxis -= 175.0f;    
textString = @"N";
[textString drawAtPoint:CGPointMake(xaxis, 65.) withFont:[UIFont fontWithName:@"Helvetica-Oblique" size:20]];

xaxis += 18.0f;
textString = @"2";
[textString drawAtPoint:CGPointMake(xaxis, 63.) withFont:[UIFont fontWithName:@"Helvetica" size:12]];

xaxis += 8.0f;
textString = @"sin";
[textString drawAtPoint:CGPointMake(xaxis, 68.) withFont:[UIFont fontWithName:@"Helvetica" size:17]];

xaxis += 20.0f;
textString = @"2";
[textString drawAtPoint:CGPointMake(xaxis, 63.) withFont:[UIFont fontWithName:@"Helvetica" size:12]];

// Inner opening bracket
xaxis += 10.0f;
textString = @"(";
[textString drawAtPoint:CGPointMake(xaxis, 64.) withFont:[UIFont fontWithName:@"Helvetica" size:22]];

xaxis += 8.0f;
unichar twelveChar[] = {0x03C0};
textString = getTextString(twelveChar, 1);
[textString drawAtPoint:CGPointMake(xaxis, 68.) withFont:[UIFont fontWithName:@"Helvetica" size:17]];

xaxis += 12.0f;
unichar thirteenChar[] = {0x2206};
textString = getTextString(thirteenChar, 1);
[textString drawAtPoint:CGPointMake(xaxis, 65.) withFont:[UIFont fontWithName:@"Helvetica" size:21]];

xaxis += 15.0f;
unichar fourteenChar[] = {0x03C9};
textString = getTextString(fourteenChar, 1);
[textString drawAtPoint:CGPointMake(xaxis, 67.) withFont:[UIFont fontWithName:@"Helvetica" size:20]];

xaxis += 15.0f;
textString = @"k";
[textString drawAtPoint:CGPointMake(xaxis, 75.) withFont:[UIFont fontWithName:@"Helvetica" size:12]];

xaxis += 8.0f;
textString = @"/";
[textString drawAtPoint:CGPointMake(xaxis, 64.) withFont:[UIFont fontWithName:@"Helvetica" size:24]];

xaxis += 8.0f;
unichar fifteenChar[] = {0x03C9};
textString = getTextString(fifteenChar, 1);
[textString drawAtPoint:CGPointMake(xaxis, 67.) withFont:[UIFont fontWithName:@"Helvetica" size:20]];

xaxis += 15.0f;
textString = @"res";
[textString drawAtPoint:CGPointMake(xaxis, 75.) withFont:[UIFont fontWithName:@"Helvetica" size:12]];

xaxis += 18.0f;
textString = @"(";
[textString drawAtPoint:CGPointMake(xaxis, 66.) withFont:[UIFont fontWithName:@"Helvetica" size:20]];

xaxis += 5.0f;
unichar sixteenChar[] = {0x03B8};
textString = getTextString(sixteenChar, 1);
[textString drawAtPoint:CGPointMake(xaxis, 66.) withFont:[UIFont fontWithName:@"Helvetica-Oblique" size:20]];

xaxis += 12.0f;
textString = @")";
[textString drawAtPoint:CGPointMake(xaxis, 66.) withFont:[UIFont fontWithName:@"Helvetica" size:20]];

// Inner closing bracket
xaxis += 6.0f;
textString = @")";
[textString drawAtPoint:CGPointMake(xaxis, 64.) withFont:[UIFont fontWithName:@"Helvetica" size:22]];

// Extra text for information
xaxis = 6.0f;
textString = @"Above is the example of an equation drawn using";
[textString drawAtPoint:CGPointMake(xaxis, 120.) withFont:[UIFont fontWithName:@"Helvetica" size:14]];
xaxis = 6.0f;
textString = @"Quartz2D";
[textString drawAtPoint:CGPointMake(xaxis, 140.) withFont:[UIFont fontWithName:@"Helvetica" size:14]];

}

static NSString *getTextString(unichar chars[], int charLength)
{   
NSString *uniString = [NSString stringWithCharacters:chars length: charLength];
return uniString;
}

【问题讨论】：

我也在寻找其他在 iPod/iPhone 中渲染数学方程式的方法 - 并发现我们可以在 UIWebView 中使用 MathML 来很好地显示它。那么在 UIWebView 中使用 Quartz2D（上面我使用的过程）和 MathML 有什么区别。
任何人都可以回复。谢谢。

标签： iphone ios cocoa-touch quartz-2d equation

【解决方案1】：

不同之处在于，您对 Web 视图的控制比您在本地执行的操作要少得多。使用 Web 视图，您可以包装其他人提出的解决方案。如果您自己做事，您将拥有更多的控制权。

【讨论】：

【解决方案2】：

如果您正在绘制有限类别的函数，例如多项式，您可以编写一个例程，将任意多项式绘制为一系列微小的连接线段。

例如

#define STEP = .05f;
draw_polynomial(context, MIN_X, MAX_X, polynomial) {
    CGFloat y = polynomial.evaluateAtX(MIN_X);
    CGContextBeginPath(context);
    CGContextMoveToPoint(context, MIN_X, y);
    for (CGFloat x = MIN_X + STEP; x < MAX_X; x += STEP){
       y = polynomial.evaluateAtX(x)
       CGContextAddLineToPoint(context, x, y);
    }
    CGContextStrokePath(context);
 }

【讨论】：