顶点数在<5时没有正多角星，顶点数>5时正多角星不唯一，本文只绘制最具代表性的一种

代码如下：

public class CanvasStar extends View{

    public CanvasStar(Context context) {
        super(context);
    }

    public CanvasStar(Context context, AttributeSet attrs) {
        super(context, attrs);
    }

    public CanvasStar(Context context, AttributeSet attrs, int defStyleAttr) {
        super(context, attrs, defStyleAttr);
    }

    public CanvasStar(Context context, AttributeSet attrs, int defStyleAttr, int defStyleRes) {
        super(context, attrs, defStyleAttr, defStyleRes);
    }

    @Override
    protected void onDraw(Canvas canvas) {
        super.onDraw(canvas);

        Paint paint=new Paint();
        paint.setAntiAlias(true);

        drawStar(canvas,paint,Color.RED,getHeight()/12,3,false);
        canvas.translate(getHeight()/6,0);
        drawStar(canvas,paint,Color.RED,getHeight()/12,3,true);
        canvas.translate(-getHeight()/6,0);
        canvas.translate(0,getHeight()/6);
        drawStar(canvas,paint,Color.YELLOW,getHeight()/12,4,false);
        canvas.translate(getHeight()/6,0);
        drawStar(canvas,paint,Color.YELLOW,getHeight()/12,4,true);
        canvas.translate(-getHeight()/6,0);
        canvas.translate(0,getHeight()/6);
        drawStar(canvas,paint,Color.GREEN,getHeight()/12,5,false);
        canvas.translate(getHeight()/6,0);
        drawStar(canvas,paint,Color.GREEN,getHeight()/12,5,true);
        canvas.translate(-getHeight()/6,0);
        canvas.translate(0,getHeight()/6);
        drawStar(canvas,paint,Color.CYAN,getHeight()/12,6,false);
        canvas.translate(getHeight()/6,0);
        drawStar(canvas,paint,Color.CYAN,getHeight()/12,6,true);
        canvas.translate(-getHeight()/6,0);
        canvas.translate(0,getHeight()/6);
        drawStar(canvas,paint,Color.BLUE,getHeight()/12,7,false);
        canvas.translate(getHeight()/6,0);
        drawStar(canvas,paint,Color.BLUE,getHeight()/12,7,true);
        canvas.translate(-getHeight()/6,0);
        canvas.translate(0,getHeight()/6);
        drawStar(canvas,paint,Color.BLACK,getHeight()/12,8,false);
        canvas.translate(getHeight()/6,0);
        drawStar(canvas,paint,Color.BLACK,getHeight()/12,8,true);
        canvas.translate(0,getHeight()/6);

    }

    /**
     * 绘制彩色多边形或星形
     * @param canvas Canvas画布
     * @param paint Paint画笔
     * @param color 颜色
     * @param radius 外接圆半径
     * @param count 外顶点数
     * @param isStar 是否为星形
     */
    private void drawStar(Canvas canvas, Paint paint, @ColorInt int color, float radius,int count,boolean isStar){
        canvas.translate(radius,radius);
        if ((!isStar) && count < 3){
            canvas.translate(-radius,-radius);
            return;
        }
        if (isStar && count < 5){
            canvas.translate(-radius,-radius);
            return;
        }
        canvas.rotate(-90);
        if (paint == null){
            paint = new Paint();
        }else{
            paint.reset();
        }
        Path path = new Path();
        float inerRadius = count%2==0?
                (radius*(cos(360/count/2)-sin(360/count/2)*sin(90-360/count)/cos(90-360/count)))
                :(radius*sin(360/count/4)/sin(180-360/count/2-360/count/4));
        for (int i=0;i<count;i++){
            if (i==0){
                path.moveTo(radius*cos(360/count*i),radius*sin(360/count*i));
            }else{
                path.lineTo(radius*cos(360/count*i),radius*sin(360/count*i));
            }
            if (isStar){
                path.lineTo(inerRadius*cos(360/count*i+360/count/2),inerRadius*sin(360/count*i+360/count/2));
            }
        }
        path.close();
        paint.setColor(color);
        canvas.drawPath(path,paint);
        canvas.rotate(90);
        canvas.translate(-radius,-radius);
    }
    
    /**
     * Math.sin的参数为弧度，使用起来不方便，重新封装一个根据角度求sin的方法
     * @param num 角度
     * @return
     */
    float sin(int num){
        return (float) Math.sin(num*Math.PI/180);
    }

    /**
     * 与sin同理
     */
    float cos(int num){
        return (float) Math.cos(num*Math.PI/180);
    }
}

效果如下：