开发过程中用不到一元一次方程吗?非也,iOS开发中经常会遇到根据某个ScrollView动态偏移量的值来实时设置一个View的透明度,你敢说你不用一元一次方程你能搞定?

想把一个动画效果做好,经常会遇到实时设置的问题,本人遇到过多次,总结出经验,提供方法来专门计算一元一次方程的K值以及b值,方便开发.

BinaryLinearEquation.h + BinaryLinearEquation.m  提供内联函数以及类方法

//  Copyright (c) 2014年 Y.X. All rights reserved.
//#import <Foundation/Foundation.h>NS_INLINE CGFloat calculateSlope(CGFloat x1, CGFloat y1, CGFloat x2, CGFloat y2)
{return (y2 - y1) / (x2 - x1);
}NS_INLINE CGFloat calculateConstant(CGFloat x1, CGFloat y1, CGFloat x2, CGFloat y2)
{return (y1*(x2 - x1) - x1*(y2 - y1)) / (x2 - x1);
}@interface BinaryLinearEquation : NSObject/*** 计算一元一次方程的斜率 K** Y = kX + b,输入两个点坐标的值(x1, y1), (x2, y2)来计算斜率k的值** @param 坐标值 两个点的坐标值(x1, y1), (x2, y2)* @return 计算得出的斜率值*/
+ (CGFloat)calculateSlopeWithX1:(CGFloat)x1 Y1:(CGFloat)y1 X2:(CGFloat)x2 Y2:(CGFloat)y2;/*** 计算一元一次方程的常数 b** Y = kX + b,输入两个点坐标的值(x1, y1), (x2, y2)来计算常数b的值** @param 坐标值 两个点的坐标值(x1, y1), (x2, y2)* @return 计算得出的常数值*/
+ (CGFloat)calculateConstantWithX1:(CGFloat)x1 Y1:(CGFloat)y1 X2:(CGFloat)x2 Y2:(CGFloat)y2;@end

//  Copyright (c) 2014年 Y.X. All rights reserved.
//#import "BinaryLinearEquation.h"@implementation BinaryLinearEquation+ (CGFloat)calculateSlopeWithX1:(CGFloat)x1 Y1:(CGFloat)y1 X2:(CGFloat)x2 Y2:(CGFloat)y2
{return (y2 - y1) / (x2 - x1);
}+ (CGFloat)calculateConstantWithX1:(CGFloat)x1 Y1:(CGFloat)y1 X2:(CGFloat)x2 Y2:(CGFloat)y2
{return (y1*(x2 - x1) - x1*(y2 - y1)) / (x2 - x1);
}@end

测试:

y = 7x - 9

k = 7

b = -9

两个点(0, -9),(9/7, 0)

---------------------------------------------------------------------------------------------

NSLog(@"%f", calculateSlope(0.f, -9.f, 9.f/7.f, 0.f));
    NSLog(@"%f", calculateConstant(0.f, -9.f, 9.f/7.f, 0.f));
    
    NSLog(@"%f", [BinaryLinearEquation calculateSlopeWithX1:0.f     Y1:-9.f
                                                         X2:9.f/7.f Y2:0.f]);
    NSLog(@"%f", [BinaryLinearEquation calculateConstantWithX1:0.f     Y1:-9.f
                                                            X2:9.f/7.f Y2:0.f]);

---------------------------------------------------------------------------------------------

2014-03-28 09:46:00.898 woobooWall[1440:60b] 7.000000
2014-03-28 09:46:00.899 woobooWall[1440:60b] -9.000000
2014-03-28 09:46:00.899 woobooWall[1440:60b] 7.000000
2014-03-28 09:46:00.899 woobooWall[1440:60b] -9.000000

使用时请将数据转换为CGFloat型.

附录1:

附录2:

根据一元一次方程组计算所有的红绿蓝透明度的斜率以及常数值

CalculateColor.h + CalculateColor.m

//
//  CalculateColor.h
//  Animation
//
//  Copyright (c) 2014年 Y.X. All rights reserved.
//#import <Foundation/Foundation.h>typedef struct ColorParam {CGFloat redSlope;         // 红色的斜率 kCGFloat redConstant;      // 红色的常数 bCGFloat greenSlope;       // 绿色的斜率 kCGFloat greenConstant;    // 绿色的常数 bCGFloat blueSlope;        // 蓝色的斜率 kCGFloat blueConstant;     // 蓝色的常数 bCGFloat alphaSlope;       // 透明度的斜率 kCGFloat alphaConstant;    // 透明度的常数 b} SColorParam;/**根据一元一次方程组计算所有的红绿蓝透明度的斜率以及常数值这是用来设计做动态设定动画效果的,需要提供起始点的UIColor,起始点的一个值,终点的UIColor,终点的一个值,然后计算出动画过程中需要的一些设置参数.@param oldColor 起始点的color@param oldPoint 起始点的值@param newColor 终点的color@param newPoint 终点的值@param param 计算好的值存储于结构体SColorParam中@return none*/
void calculateUIColorAndPoint(UIColor *oldColor,CGFloat oldPoint,UIColor *newColor, CGFloat newPoint,SColorParam *param);

//
//  CalculateColor.m
//  Animation
//
//  Copyright (c) 2014年 Y.X. All rights reserved.
//#import "CalculateColor.h"#pragma mark - 计算斜率 k
CGFloat calculateSlope(CGFloat x1, CGFloat y1, CGFloat x2, CGFloat y2)
{return (y2 - y1) / (x2 - x1);
}#pragma mark - 计算常数 b
CGFloat calculateConstant(CGFloat x1, CGFloat y1, CGFloat x2, CGFloat y2)
{return (y1*(x2 - x1) - x1*(y2 - y1)) / (x2 - x1);
}#pragma mark - 根据一元一次方程组计算所有的红绿蓝透明度的斜率以及常数值
void calculateUIColorAndPoint(UIColor *oldColor,CGFloat oldPoint,UIColor *newColor, CGFloat newPoint,SColorParam *param)
{// 获取旧颜色CGFloat oldRed    = 0;CGFloat oldGreen  = 0;CGFloat oldBlue   = 0;CGFloat oldAlpha  = 0;[oldColor getRed:&oldRed green:&oldGreen blue:&oldBlue alpha:&oldAlpha];// 获取新颜色CGFloat newRed    = 0;CGFloat newGreen  = 0;CGFloat newBlue   = 0;CGFloat newAlpha  = 0;[newColor getRed:&newRed green:&newGreen blue:&newBlue alpha:&newAlpha];// 计算每一个k值和b值param->redSlope       = calculateSlope(oldPoint, oldRed, newPoint, newRed);param->redConstant    = calculateConstant(oldPoint, oldRed, newPoint, newRed);param->greenSlope     = calculateSlope(oldPoint, oldGreen, newPoint, newGreen);param->greenConstant  = calculateConstant(oldPoint, oldGreen, newPoint, newGreen);param->blueSlope      = calculateSlope(oldPoint, oldBlue, newPoint, newBlue);param->blueConstant   = calculateConstant(oldPoint, oldBlue, newPoint, newBlue);param->alphaSlope     = calculateSlope(oldPoint, oldAlpha, newPoint, newAlpha);param->alphaConstant  = calculateConstant(oldPoint, oldAlpha, newPoint, newAlpha);
}

以下是实现动态改变颜色的方法

#import "YX_2_ViewController.h"
#import "CalculateColor.h"@interface YX_2_ViewController ()<UIScrollViewDelegate>@property (strong, nonatomic) UIScrollView  *mainScrollView;@end@implementation YX_2_ViewController- (void)viewDidLoad
{[super viewDidLoad];_mainScrollView = [[UIScrollView alloc] initWithFrame:self.view.bounds];_mainScrollView.contentSize = CGSizeMake(self.view.bounds.size.width * 2,self.view.bounds.size.height);_mainScrollView.backgroundColor = [UIColor cyanColor];_mainScrollView.delegate = self;[self.view addSubview:_mainScrollView];
}- (void)scrollViewDidScroll:(UIScrollView *)scrollView
{static SColorParam paramVe2 = {0};// 只计算一次static int flag = 0;if (flag == 0) {calculateUIColorAndPoint([UIColor cyanColor],0,[UIColor redColor],320, ¶mVe2);flag = 1;}UIColor *color =[UIColor colorWithRed:scrollView.contentOffset.x * paramVe2.redSlope + paramVe2.redConstantgreen:scrollView.contentOffset.x * paramVe2.greenSlope + paramVe2.greenConstantblue:scrollView.contentOffset.x * paramVe2.blueSlope + paramVe2.blueConstantalpha:1];scrollView.backgroundColor = color;
}@end