您好,登錄后才能下訂單哦!
心形線
心形線,是一個圓上的固定一點在它繞著與其相切且半徑相同的另外一個圓周滾動時所形成的軌跡,因其形狀像心形而得名。
心臟線亦為蚶線的一種。在曼德博集合正中間的圖形便是一個心臟線。心臟線的英文名稱“Cardioid”是 de Castillon 在1741年的《Philosophical Transactions of the Royal Society》發表的;意為“像心臟的”。
極坐標方程
水平方向: ρ=a(1-cosθ) 或 ρ=a(1+cosθ) (a>0)
垂直方向: ρ=a(1-sinθ) 或 ρ=a(1+sinθ) (a>0)
直角坐標方程
心形線的平面直角坐標系方程表達式分別為 x^2+y^2+a*x=a*sqrt(x^2+y^2) 和 x^2+y^2-a*x=a*sqrt(x^2+y^2)
參數方程
x=a*(2*cos(t)-cos(2*t))
y=a*(2*sin(t)-sin(2*t))
所圍面積為3/2*PI*a^2,形成的弧長為8a
通過不同變換可以有如下樣式
解題思路
在直角坐標系中x、y軸的正方向分別是右側和上方,原點在中間;而在命令行中正方向分別是右方和下方,原點在左上角。因此就需要進行坐標軸變換。
由于直角坐標系中的心形線是橫著的,因此需要x<->y軸的變換。
由于在命令行具有行高這一固定參數,因此同樣字符數的行和列長度是不同的(行會比列短很多),因此又需要進行控制臺x軸的拉伸操作。
C++代碼
#include <iostream> #include <math.h> using namespace std; #define X_DIVIDED_BY_Y 0.5 #define MAX_X (35.0 / X_DIVIDED_BY_Y) #define MAX_Y 35.0 #define THRESHOLD 0.5 #define A 13 char getSentenceChar(const char *sentence, int &index) { while(true) { if (index >= strlen(sentence)) { index = 0; } char c = sentence[index++]; if(' ' == c) { index++; } else { return c; } } } inline float getX(float x) { return (x - MAX_X / 2) * X_DIVIDED_BY_Y; } inline float getY(float y) { return MAX_Y / 7.0 - y; } bool func(float x, float y) { return (pow(x, 2) + pow(y, 2) + A * x - A * sqrt(pow(x, 2) + pow(y, 2))) < THRESHOLD; } void main(int argc, char** argv) { const char *LOVE_SENTENCE = "No rose, no diamond ring, that is the simple and romantic love stories in college. The graduates have to face the approaching of June, a time to farewell their beloved. When their future is confronted with love, which one is more important? What will the lovers do in June?"; int sentenceIndex = 0; for (int y = 0; y <= MAX_Y; y++) { for (int x = 0; x <= MAX_X; x++) { cout<<(func(getY(y), getX(x)) ? getSentenceChar(LOVE_SENTENCE, sentenceIndex) : '.'); } cout<<endl; } }
Java代碼
package com.example.demo; public class BenevolenceDemo { private static final float X_DIVIDED_BY_Y = 0.5f; private static final float MAX_X = 35f / X_DIVIDED_BY_Y; private static final float MAX_Y = 35f; private static final float THRESHOLD = 0.5f; private static final float A = 13; private static final String LOVE_SENTENCE = "No rose, no diamond ring, that is the simple and romantic love stories in college. The graduates have to face the approaching of June, a time to farewell their beloved. When their future is confronted with love, which one is more important? What will the lovers do in June?"; private static int sentenceIndex = 0; private static char getSentenceChar() { while(true) { if (sentenceIndex >= LOVE_SENTENCE.length()) { sentenceIndex = 0; } char c = LOVE_SENTENCE.charAt(sentenceIndex++); if(' ' == c) { sentenceIndex++; } else { return c; } } } public static void main(String[] args) { for (int y = 0; y <= MAX_Y; y++) { for (int x = 0; x <= MAX_X; x++) { System.out.print(func(getY(y), getX(x)) ? getSentenceChar() : '='); } System.out.println(); } } public static final float getX(float x) { return (x - MAX_X / 2) * X_DIVIDED_BY_Y; } public static final float getY(float y) { return MAX_Y / 7f - y; } public static boolean func(float x, float y) { return (Math.pow(x, 2) + Math.pow(y, 2) + A * x - A * Math.sqrt(Math.pow(x, 2) + Math.pow(y, 2))) < THRESHOLD; } }
以上就是本文的全部內容,希望對大家的學習有所幫助,也希望大家多多支持億速云。
免責聲明:本站發布的內容(圖片、視頻和文字)以原創、轉載和分享為主,文章觀點不代表本網站立場,如果涉及侵權請聯系站長郵箱:is@yisu.com進行舉報,并提供相關證據,一經查實,將立刻刪除涉嫌侵權內容。