Drawing lines using RequestAnimationFrame()
.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty{ height:90px;width:728px;box-sizing:border-box;
}
I want to draw a horizontal line when the game launches and was able to come up with something that drew the line using requestAnimationFrame()
and ctx.stroke()
.
The problem is that when I attempt to edit the length of the line by changing the values of the end point on the line, the line remains the same length.
If anyone could take a look at it and explain what is going on I would really appreciate it.
var canvasTop = document.getElementById('top');
var ctxTop = canvasTop.getContext('2d');
var frameCountTop = 0;
var fpsTop, fpsIntervalTop, startTimeTop, nowTop, thenTop, elapsedTop;
function startAnimatingTop(fpsTop) {
fpsIntervalTop = 1000 / fpsTop;
thenTop = Date.now();
startTimeTop = thenTop;
drawTop();
}
var topLinePointA = [32, 80];
var topLinePointB = [280, 80];
var topLineStart = topLinePointA[0];
var topLineIncrement = topLineStart + 1;
var topLineEnd = topLinePointB[0];
function drawTop() {
var i = 32;
while (i < topLineEnd) {
requestAnimationFrame(drawTop);
i++;
nowTop = Date.now();
elapsedTop = nowTop - thenTop;
if (elapsedTop > fpsIntervalTop && i < topLineEnd) {
thenTop = nowTop - (elapsedTop % fpsIntervalTop);
ctxTop.lineWidth = 20;
ctxTop.strokeStyle = "black";
ctxTop.moveTo(topLineStart, 80);
ctxTop.lineTo(topLineIncrement, 80);
ctxTop.stroke();
topLineStart += 1;
} else {
cancelAnimationFrame(drawTop);
return;
}
}
}
startAnimatingTop(100);
/*HANGMAN STYLES*/
/*CLASS SELECTORS*/
.lineContainer {
/*border-style: solid;
border-color: blue;*/
}
#top {
position: absolute;
height: 5%;
width: 45%;
left: 30%;
}
#side {
position: absolute;
bottom: 20%;
left: 70%;
height: 78%;
width: 5%;
}
#bottom {
position: absolute;
bottom: 35%;
height: 5%;
width: 56%;
left: 20%;
}
#hangman {
position: absolute;
left: 30%;
height: 40%;
width: 10%;
}
<canvas id='top' class='lineContainer'></canvas>
<canvas id='side' class='lineContainer'></canvas>
<canvas id='bottom' class='lineContainer'></canvas>
<canvas id='hangman' class='lineContainer'></canvas>
<canvas id='puzzle'></canvas>
<div id='scorecard'>
</div>
javascript animation html5-canvas
add a comment |
I want to draw a horizontal line when the game launches and was able to come up with something that drew the line using requestAnimationFrame()
and ctx.stroke()
.
The problem is that when I attempt to edit the length of the line by changing the values of the end point on the line, the line remains the same length.
If anyone could take a look at it and explain what is going on I would really appreciate it.
var canvasTop = document.getElementById('top');
var ctxTop = canvasTop.getContext('2d');
var frameCountTop = 0;
var fpsTop, fpsIntervalTop, startTimeTop, nowTop, thenTop, elapsedTop;
function startAnimatingTop(fpsTop) {
fpsIntervalTop = 1000 / fpsTop;
thenTop = Date.now();
startTimeTop = thenTop;
drawTop();
}
var topLinePointA = [32, 80];
var topLinePointB = [280, 80];
var topLineStart = topLinePointA[0];
var topLineIncrement = topLineStart + 1;
var topLineEnd = topLinePointB[0];
function drawTop() {
var i = 32;
while (i < topLineEnd) {
requestAnimationFrame(drawTop);
i++;
nowTop = Date.now();
elapsedTop = nowTop - thenTop;
if (elapsedTop > fpsIntervalTop && i < topLineEnd) {
thenTop = nowTop - (elapsedTop % fpsIntervalTop);
ctxTop.lineWidth = 20;
ctxTop.strokeStyle = "black";
ctxTop.moveTo(topLineStart, 80);
ctxTop.lineTo(topLineIncrement, 80);
ctxTop.stroke();
topLineStart += 1;
} else {
cancelAnimationFrame(drawTop);
return;
}
}
}
startAnimatingTop(100);
/*HANGMAN STYLES*/
/*CLASS SELECTORS*/
.lineContainer {
/*border-style: solid;
border-color: blue;*/
}
#top {
position: absolute;
height: 5%;
width: 45%;
left: 30%;
}
#side {
position: absolute;
bottom: 20%;
left: 70%;
height: 78%;
width: 5%;
}
#bottom {
position: absolute;
bottom: 35%;
height: 5%;
width: 56%;
left: 20%;
}
#hangman {
position: absolute;
left: 30%;
height: 40%;
width: 10%;
}
<canvas id='top' class='lineContainer'></canvas>
<canvas id='side' class='lineContainer'></canvas>
<canvas id='bottom' class='lineContainer'></canvas>
<canvas id='hangman' class='lineContainer'></canvas>
<canvas id='puzzle'></canvas>
<div id='scorecard'>
</div>
javascript animation html5-canvas
add a comment |
I want to draw a horizontal line when the game launches and was able to come up with something that drew the line using requestAnimationFrame()
and ctx.stroke()
.
The problem is that when I attempt to edit the length of the line by changing the values of the end point on the line, the line remains the same length.
If anyone could take a look at it and explain what is going on I would really appreciate it.
var canvasTop = document.getElementById('top');
var ctxTop = canvasTop.getContext('2d');
var frameCountTop = 0;
var fpsTop, fpsIntervalTop, startTimeTop, nowTop, thenTop, elapsedTop;
function startAnimatingTop(fpsTop) {
fpsIntervalTop = 1000 / fpsTop;
thenTop = Date.now();
startTimeTop = thenTop;
drawTop();
}
var topLinePointA = [32, 80];
var topLinePointB = [280, 80];
var topLineStart = topLinePointA[0];
var topLineIncrement = topLineStart + 1;
var topLineEnd = topLinePointB[0];
function drawTop() {
var i = 32;
while (i < topLineEnd) {
requestAnimationFrame(drawTop);
i++;
nowTop = Date.now();
elapsedTop = nowTop - thenTop;
if (elapsedTop > fpsIntervalTop && i < topLineEnd) {
thenTop = nowTop - (elapsedTop % fpsIntervalTop);
ctxTop.lineWidth = 20;
ctxTop.strokeStyle = "black";
ctxTop.moveTo(topLineStart, 80);
ctxTop.lineTo(topLineIncrement, 80);
ctxTop.stroke();
topLineStart += 1;
} else {
cancelAnimationFrame(drawTop);
return;
}
}
}
startAnimatingTop(100);
/*HANGMAN STYLES*/
/*CLASS SELECTORS*/
.lineContainer {
/*border-style: solid;
border-color: blue;*/
}
#top {
position: absolute;
height: 5%;
width: 45%;
left: 30%;
}
#side {
position: absolute;
bottom: 20%;
left: 70%;
height: 78%;
width: 5%;
}
#bottom {
position: absolute;
bottom: 35%;
height: 5%;
width: 56%;
left: 20%;
}
#hangman {
position: absolute;
left: 30%;
height: 40%;
width: 10%;
}
<canvas id='top' class='lineContainer'></canvas>
<canvas id='side' class='lineContainer'></canvas>
<canvas id='bottom' class='lineContainer'></canvas>
<canvas id='hangman' class='lineContainer'></canvas>
<canvas id='puzzle'></canvas>
<div id='scorecard'>
</div>
javascript animation html5-canvas
I want to draw a horizontal line when the game launches and was able to come up with something that drew the line using requestAnimationFrame()
and ctx.stroke()
.
The problem is that when I attempt to edit the length of the line by changing the values of the end point on the line, the line remains the same length.
If anyone could take a look at it and explain what is going on I would really appreciate it.
var canvasTop = document.getElementById('top');
var ctxTop = canvasTop.getContext('2d');
var frameCountTop = 0;
var fpsTop, fpsIntervalTop, startTimeTop, nowTop, thenTop, elapsedTop;
function startAnimatingTop(fpsTop) {
fpsIntervalTop = 1000 / fpsTop;
thenTop = Date.now();
startTimeTop = thenTop;
drawTop();
}
var topLinePointA = [32, 80];
var topLinePointB = [280, 80];
var topLineStart = topLinePointA[0];
var topLineIncrement = topLineStart + 1;
var topLineEnd = topLinePointB[0];
function drawTop() {
var i = 32;
while (i < topLineEnd) {
requestAnimationFrame(drawTop);
i++;
nowTop = Date.now();
elapsedTop = nowTop - thenTop;
if (elapsedTop > fpsIntervalTop && i < topLineEnd) {
thenTop = nowTop - (elapsedTop % fpsIntervalTop);
ctxTop.lineWidth = 20;
ctxTop.strokeStyle = "black";
ctxTop.moveTo(topLineStart, 80);
ctxTop.lineTo(topLineIncrement, 80);
ctxTop.stroke();
topLineStart += 1;
} else {
cancelAnimationFrame(drawTop);
return;
}
}
}
startAnimatingTop(100);
/*HANGMAN STYLES*/
/*CLASS SELECTORS*/
.lineContainer {
/*border-style: solid;
border-color: blue;*/
}
#top {
position: absolute;
height: 5%;
width: 45%;
left: 30%;
}
#side {
position: absolute;
bottom: 20%;
left: 70%;
height: 78%;
width: 5%;
}
#bottom {
position: absolute;
bottom: 35%;
height: 5%;
width: 56%;
left: 20%;
}
#hangman {
position: absolute;
left: 30%;
height: 40%;
width: 10%;
}
<canvas id='top' class='lineContainer'></canvas>
<canvas id='side' class='lineContainer'></canvas>
<canvas id='bottom' class='lineContainer'></canvas>
<canvas id='hangman' class='lineContainer'></canvas>
<canvas id='puzzle'></canvas>
<div id='scorecard'>
</div>
var canvasTop = document.getElementById('top');
var ctxTop = canvasTop.getContext('2d');
var frameCountTop = 0;
var fpsTop, fpsIntervalTop, startTimeTop, nowTop, thenTop, elapsedTop;
function startAnimatingTop(fpsTop) {
fpsIntervalTop = 1000 / fpsTop;
thenTop = Date.now();
startTimeTop = thenTop;
drawTop();
}
var topLinePointA = [32, 80];
var topLinePointB = [280, 80];
var topLineStart = topLinePointA[0];
var topLineIncrement = topLineStart + 1;
var topLineEnd = topLinePointB[0];
function drawTop() {
var i = 32;
while (i < topLineEnd) {
requestAnimationFrame(drawTop);
i++;
nowTop = Date.now();
elapsedTop = nowTop - thenTop;
if (elapsedTop > fpsIntervalTop && i < topLineEnd) {
thenTop = nowTop - (elapsedTop % fpsIntervalTop);
ctxTop.lineWidth = 20;
ctxTop.strokeStyle = "black";
ctxTop.moveTo(topLineStart, 80);
ctxTop.lineTo(topLineIncrement, 80);
ctxTop.stroke();
topLineStart += 1;
} else {
cancelAnimationFrame(drawTop);
return;
}
}
}
startAnimatingTop(100);
/*HANGMAN STYLES*/
/*CLASS SELECTORS*/
.lineContainer {
/*border-style: solid;
border-color: blue;*/
}
#top {
position: absolute;
height: 5%;
width: 45%;
left: 30%;
}
#side {
position: absolute;
bottom: 20%;
left: 70%;
height: 78%;
width: 5%;
}
#bottom {
position: absolute;
bottom: 35%;
height: 5%;
width: 56%;
left: 20%;
}
#hangman {
position: absolute;
left: 30%;
height: 40%;
width: 10%;
}
<canvas id='top' class='lineContainer'></canvas>
<canvas id='side' class='lineContainer'></canvas>
<canvas id='bottom' class='lineContainer'></canvas>
<canvas id='hangman' class='lineContainer'></canvas>
<canvas id='puzzle'></canvas>
<div id='scorecard'>
</div>
var canvasTop = document.getElementById('top');
var ctxTop = canvasTop.getContext('2d');
var frameCountTop = 0;
var fpsTop, fpsIntervalTop, startTimeTop, nowTop, thenTop, elapsedTop;
function startAnimatingTop(fpsTop) {
fpsIntervalTop = 1000 / fpsTop;
thenTop = Date.now();
startTimeTop = thenTop;
drawTop();
}
var topLinePointA = [32, 80];
var topLinePointB = [280, 80];
var topLineStart = topLinePointA[0];
var topLineIncrement = topLineStart + 1;
var topLineEnd = topLinePointB[0];
function drawTop() {
var i = 32;
while (i < topLineEnd) {
requestAnimationFrame(drawTop);
i++;
nowTop = Date.now();
elapsedTop = nowTop - thenTop;
if (elapsedTop > fpsIntervalTop && i < topLineEnd) {
thenTop = nowTop - (elapsedTop % fpsIntervalTop);
ctxTop.lineWidth = 20;
ctxTop.strokeStyle = "black";
ctxTop.moveTo(topLineStart, 80);
ctxTop.lineTo(topLineIncrement, 80);
ctxTop.stroke();
topLineStart += 1;
} else {
cancelAnimationFrame(drawTop);
return;
}
}
}
startAnimatingTop(100);
/*HANGMAN STYLES*/
/*CLASS SELECTORS*/
.lineContainer {
/*border-style: solid;
border-color: blue;*/
}
#top {
position: absolute;
height: 5%;
width: 45%;
left: 30%;
}
#side {
position: absolute;
bottom: 20%;
left: 70%;
height: 78%;
width: 5%;
}
#bottom {
position: absolute;
bottom: 35%;
height: 5%;
width: 56%;
left: 20%;
}
#hangman {
position: absolute;
left: 30%;
height: 40%;
width: 10%;
}
<canvas id='top' class='lineContainer'></canvas>
<canvas id='side' class='lineContainer'></canvas>
<canvas id='bottom' class='lineContainer'></canvas>
<canvas id='hangman' class='lineContainer'></canvas>
<canvas id='puzzle'></canvas>
<div id='scorecard'>
</div>
javascript animation html5-canvas
javascript animation html5-canvas
edited Nov 23 '18 at 19:09
ggorlen
7,9633926
7,9633926
asked Nov 23 '18 at 18:55
LarryYoungLarryYoung
207
207
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
There are many problems with your code.
You need to read up on using the canvas. https://developer.mozilla.org/en-US/docs/Web/API/CanvasRenderingContext2D will help.
- Only call
requestAnimationFrame
once per frame. Putting it inside a while loop will just start 1000's of frames fighting for display refresh. - Start paths with
ctx.beginPath();
- Clear the canvas using
ctx.clearRect(0,0,width,height)
- Set canvas size via attributes not via style properties.
- The first argument to the function called by
requestAnimationFrame
is the time. egdrawTop(time)
See comments for more info.
ctx.canvas.width = 100; // << set the canvas size via canvas attributes not style
ctx.canvas.height = 100;
var thenTop = performance.now(); // to get time.
requestAnimationFrame(drawTop); // <<< start the render loop with request, dont call direct
function drawTop(nowTop) { // << time passed to render call
requestAnimationFrame(drawTop); // <<< put call here not in loop
ctxTop.clearRect(0, 0, ctxTop.canvas.width, ctxTop.canvas.height); // <<< clear the canvas
var i = 32;
while (i < topLineEnd) {
// requestAnimationFrame(drawTop); // <<<<<<< Not here
i++;
elapsedTop = nowTop - thenTop;
if (elapsedTop > fpsIntervalTop && i < topLineEnd) {
thenTop = nowTop - (elapsedTop % fpsIntervalTop);
ctxTop.lineWidth = 20;
ctxTop.strokeStyle = "black";
ctxTop.beginPath(); // <<<<<< To start a new path
ctxTop.moveTo(topLineStart, 80);
ctxTop.lineTo(topLineIncrement, 80);
ctxTop.stroke();
topLineStart += 1;
} else {
return;
}
}
}
Thanks I'll go back and do some more studying on the mdn and maybe post an update. I really appreciate you taking the time to do the rewrite. it will help alot!
– LarryYoung
Nov 23 '18 at 22:35
good explanations and visuals. Easy to understand. Thanks again
– LarryYoung
Nov 23 '18 at 23:17
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
There are many problems with your code.
You need to read up on using the canvas. https://developer.mozilla.org/en-US/docs/Web/API/CanvasRenderingContext2D will help.
- Only call
requestAnimationFrame
once per frame. Putting it inside a while loop will just start 1000's of frames fighting for display refresh. - Start paths with
ctx.beginPath();
- Clear the canvas using
ctx.clearRect(0,0,width,height)
- Set canvas size via attributes not via style properties.
- The first argument to the function called by
requestAnimationFrame
is the time. egdrawTop(time)
See comments for more info.
ctx.canvas.width = 100; // << set the canvas size via canvas attributes not style
ctx.canvas.height = 100;
var thenTop = performance.now(); // to get time.
requestAnimationFrame(drawTop); // <<< start the render loop with request, dont call direct
function drawTop(nowTop) { // << time passed to render call
requestAnimationFrame(drawTop); // <<< put call here not in loop
ctxTop.clearRect(0, 0, ctxTop.canvas.width, ctxTop.canvas.height); // <<< clear the canvas
var i = 32;
while (i < topLineEnd) {
// requestAnimationFrame(drawTop); // <<<<<<< Not here
i++;
elapsedTop = nowTop - thenTop;
if (elapsedTop > fpsIntervalTop && i < topLineEnd) {
thenTop = nowTop - (elapsedTop % fpsIntervalTop);
ctxTop.lineWidth = 20;
ctxTop.strokeStyle = "black";
ctxTop.beginPath(); // <<<<<< To start a new path
ctxTop.moveTo(topLineStart, 80);
ctxTop.lineTo(topLineIncrement, 80);
ctxTop.stroke();
topLineStart += 1;
} else {
return;
}
}
}
Thanks I'll go back and do some more studying on the mdn and maybe post an update. I really appreciate you taking the time to do the rewrite. it will help alot!
– LarryYoung
Nov 23 '18 at 22:35
good explanations and visuals. Easy to understand. Thanks again
– LarryYoung
Nov 23 '18 at 23:17
add a comment |
There are many problems with your code.
You need to read up on using the canvas. https://developer.mozilla.org/en-US/docs/Web/API/CanvasRenderingContext2D will help.
- Only call
requestAnimationFrame
once per frame. Putting it inside a while loop will just start 1000's of frames fighting for display refresh. - Start paths with
ctx.beginPath();
- Clear the canvas using
ctx.clearRect(0,0,width,height)
- Set canvas size via attributes not via style properties.
- The first argument to the function called by
requestAnimationFrame
is the time. egdrawTop(time)
See comments for more info.
ctx.canvas.width = 100; // << set the canvas size via canvas attributes not style
ctx.canvas.height = 100;
var thenTop = performance.now(); // to get time.
requestAnimationFrame(drawTop); // <<< start the render loop with request, dont call direct
function drawTop(nowTop) { // << time passed to render call
requestAnimationFrame(drawTop); // <<< put call here not in loop
ctxTop.clearRect(0, 0, ctxTop.canvas.width, ctxTop.canvas.height); // <<< clear the canvas
var i = 32;
while (i < topLineEnd) {
// requestAnimationFrame(drawTop); // <<<<<<< Not here
i++;
elapsedTop = nowTop - thenTop;
if (elapsedTop > fpsIntervalTop && i < topLineEnd) {
thenTop = nowTop - (elapsedTop % fpsIntervalTop);
ctxTop.lineWidth = 20;
ctxTop.strokeStyle = "black";
ctxTop.beginPath(); // <<<<<< To start a new path
ctxTop.moveTo(topLineStart, 80);
ctxTop.lineTo(topLineIncrement, 80);
ctxTop.stroke();
topLineStart += 1;
} else {
return;
}
}
}
Thanks I'll go back and do some more studying on the mdn and maybe post an update. I really appreciate you taking the time to do the rewrite. it will help alot!
– LarryYoung
Nov 23 '18 at 22:35
good explanations and visuals. Easy to understand. Thanks again
– LarryYoung
Nov 23 '18 at 23:17
add a comment |
There are many problems with your code.
You need to read up on using the canvas. https://developer.mozilla.org/en-US/docs/Web/API/CanvasRenderingContext2D will help.
- Only call
requestAnimationFrame
once per frame. Putting it inside a while loop will just start 1000's of frames fighting for display refresh. - Start paths with
ctx.beginPath();
- Clear the canvas using
ctx.clearRect(0,0,width,height)
- Set canvas size via attributes not via style properties.
- The first argument to the function called by
requestAnimationFrame
is the time. egdrawTop(time)
See comments for more info.
ctx.canvas.width = 100; // << set the canvas size via canvas attributes not style
ctx.canvas.height = 100;
var thenTop = performance.now(); // to get time.
requestAnimationFrame(drawTop); // <<< start the render loop with request, dont call direct
function drawTop(nowTop) { // << time passed to render call
requestAnimationFrame(drawTop); // <<< put call here not in loop
ctxTop.clearRect(0, 0, ctxTop.canvas.width, ctxTop.canvas.height); // <<< clear the canvas
var i = 32;
while (i < topLineEnd) {
// requestAnimationFrame(drawTop); // <<<<<<< Not here
i++;
elapsedTop = nowTop - thenTop;
if (elapsedTop > fpsIntervalTop && i < topLineEnd) {
thenTop = nowTop - (elapsedTop % fpsIntervalTop);
ctxTop.lineWidth = 20;
ctxTop.strokeStyle = "black";
ctxTop.beginPath(); // <<<<<< To start a new path
ctxTop.moveTo(topLineStart, 80);
ctxTop.lineTo(topLineIncrement, 80);
ctxTop.stroke();
topLineStart += 1;
} else {
return;
}
}
}
There are many problems with your code.
You need to read up on using the canvas. https://developer.mozilla.org/en-US/docs/Web/API/CanvasRenderingContext2D will help.
- Only call
requestAnimationFrame
once per frame. Putting it inside a while loop will just start 1000's of frames fighting for display refresh. - Start paths with
ctx.beginPath();
- Clear the canvas using
ctx.clearRect(0,0,width,height)
- Set canvas size via attributes not via style properties.
- The first argument to the function called by
requestAnimationFrame
is the time. egdrawTop(time)
See comments for more info.
ctx.canvas.width = 100; // << set the canvas size via canvas attributes not style
ctx.canvas.height = 100;
var thenTop = performance.now(); // to get time.
requestAnimationFrame(drawTop); // <<< start the render loop with request, dont call direct
function drawTop(nowTop) { // << time passed to render call
requestAnimationFrame(drawTop); // <<< put call here not in loop
ctxTop.clearRect(0, 0, ctxTop.canvas.width, ctxTop.canvas.height); // <<< clear the canvas
var i = 32;
while (i < topLineEnd) {
// requestAnimationFrame(drawTop); // <<<<<<< Not here
i++;
elapsedTop = nowTop - thenTop;
if (elapsedTop > fpsIntervalTop && i < topLineEnd) {
thenTop = nowTop - (elapsedTop % fpsIntervalTop);
ctxTop.lineWidth = 20;
ctxTop.strokeStyle = "black";
ctxTop.beginPath(); // <<<<<< To start a new path
ctxTop.moveTo(topLineStart, 80);
ctxTop.lineTo(topLineIncrement, 80);
ctxTop.stroke();
topLineStart += 1;
} else {
return;
}
}
}
answered Nov 23 '18 at 19:34
Blindman67Blindman67
27.3k52764
27.3k52764
Thanks I'll go back and do some more studying on the mdn and maybe post an update. I really appreciate you taking the time to do the rewrite. it will help alot!
– LarryYoung
Nov 23 '18 at 22:35
good explanations and visuals. Easy to understand. Thanks again
– LarryYoung
Nov 23 '18 at 23:17
add a comment |
Thanks I'll go back and do some more studying on the mdn and maybe post an update. I really appreciate you taking the time to do the rewrite. it will help alot!
– LarryYoung
Nov 23 '18 at 22:35
good explanations and visuals. Easy to understand. Thanks again
– LarryYoung
Nov 23 '18 at 23:17
Thanks I'll go back and do some more studying on the mdn and maybe post an update. I really appreciate you taking the time to do the rewrite. it will help alot!
– LarryYoung
Nov 23 '18 at 22:35
Thanks I'll go back and do some more studying on the mdn and maybe post an update. I really appreciate you taking the time to do the rewrite. it will help alot!
– LarryYoung
Nov 23 '18 at 22:35
good explanations and visuals. Easy to understand. Thanks again
– LarryYoung
Nov 23 '18 at 23:17
good explanations and visuals. Easy to understand. Thanks again
– LarryYoung
Nov 23 '18 at 23:17
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