From b3c098fbb5bc0f64feda8d20e0dafb91f00aa20a Mon Sep 17 00:00:00 2001 From: Abel Tim Date: Sun, 30 Jun 2024 17:38:05 +0200 Subject: motor drivers --- debug/IMU_comp/IMU_comp.ino | 25 +- debug/motordriver/kiwidrive_calc.svg | 323 ++++++++ debug/motordriver/nomultiplexer/nomultiplexer.ino | 294 ++++--- debug/motordriver/onemotor/onemotor.ino | 88 +++ poster.svg | 885 +--------------------- 5 files changed, 620 insertions(+), 995 deletions(-) create mode 100644 debug/motordriver/kiwidrive_calc.svg create mode 100644 debug/motordriver/onemotor/onemotor.ino diff --git a/debug/IMU_comp/IMU_comp.ino b/debug/IMU_comp/IMU_comp.ino index 40d99b6..0c3928d 100644 --- a/debug/IMU_comp/IMU_comp.ino +++ b/debug/IMU_comp/IMU_comp.ino @@ -1,11 +1,9 @@ -//https://www.pololu.com/product/2862 #include #include +#include LIS3MDL mag; -char report[80]; - void setup() { Serial.begin(9600); @@ -24,9 +22,24 @@ void loop() { mag.read(); - snprintf(report, sizeof(report), "M: %6d %6d %6d", - mag.m.x, mag.m.y, mag.m.z); - Serial.println(report); + // Calculate heading + float heading = atan2(mag.m.y, mag.m.x); + if (heading < 0) + heading += 2 * PI; // Normalize heading to positive angles + + // Convert from radians to degrees + float headingDegrees = heading * 180.0 / PI; + + // Adjust for magnetic declination if needed + // headingDegrees += magneticDeclination; + + // Normalize headingDegrees to [0, 360) range + if (headingDegrees >= 360.0) + headingDegrees -= 360.0; + + // Print heading + Serial.print("Heading: "); + Serial.println(headingDegrees); delay(100); } diff --git a/debug/motordriver/kiwidrive_calc.svg b/debug/motordriver/kiwidrive_calc.svg new file mode 100644 index 0000000..3ca09e2 --- /dev/null +++ b/debug/motordriver/kiwidrive_calc.svg @@ -0,0 +1,323 @@ + + + + + + + + image/svg+xml + + + + + + + + + + + + + x + y + 0 + 1 + 1 + -1 + -1 + + 0rad + 2.09rad + 4.18rad + A + B + C + + + + 0.52rad + + + diff --git a/debug/motordriver/nomultiplexer/nomultiplexer.ino b/debug/motordriver/nomultiplexer/nomultiplexer.ino index d2800a8..4ca1ca8 100644 --- a/debug/motordriver/nomultiplexer/nomultiplexer.ino +++ b/debug/motordriver/nomultiplexer/nomultiplexer.ino @@ -2,25 +2,29 @@ //https://www.pololu.com/product/2997 //https://www.pololu.com/product/4861 // -// motor one -int m1penA = 1; +// motor one/A front +int m1enA = 1; int m1enB = 2; int m1pwm1 = 3; int m1pwm2 = 4; int m1encA = 13; int m1encB = 14; -// motor two +// motor two/B left int m2enA = 5; int m2enB = 6; int m2pwm1 = 7; int m2pwm2 = 8; -// motor three +int m2encA = 15; +int m2encB = 16; +// motor three/C right int m3enA = 9; int m3enB = 10; int m3pwm1 = 11; int m3pwm2 = 12; +int m3encA = 17; +int m3encB = 18; -int sp = 160; +double sp = 1.000; //speed in 0-1 double dirA = 0.00; double dirB = 0.00; @@ -29,6 +33,23 @@ double spdA = 0.00; double spdB = 0.00; double spdC = 0.00; double dirrad = 0.00; +double pi = 3.1415926535897; + +double Arpm = 0.00; +volatile long Aencount = 0; +unsigned long ALtime = 0; +unsigned long ACtime = 0; +unsigned long APtime = 0; +double Brpm = 0.00; +volatile long Bencount = 0; +unsigned long BLtime = 0; +unsigned long BCtime = 0; +unsigned long BPtime = 0; +double Crpm = 0.00; +volatile long Cencount = 0; +unsigned long CLtime = 0; +unsigned long CCtime = 0; +unsigned long CPtime = 0; void setup() { @@ -47,146 +68,189 @@ void setup() pinMode(m3pwm1, OUTPUT); pinMode(m3pwm2, OUTPUT); + //set encoder pins to input pinMode(m1encA, INPUT); pinMode(m1encB, INPUT); + pinMode(m2encA, INPUT); + pinMode(m2encB, INPUT); + pinMode(m3encA, INPUT); + pinMode(m3encB, INPUT); + attachInterrupt(digitalPinToInterrupt(m1encA), AencoderISR, CHANGE); + attachInterrupt(digitalPinToInterrupt(m1encB), AencoderISR, CHANGE); + attachInterrupt(digitalPinToInterrupt(m2encA), BencoderISR, CHANGE); + attachInterrupt(digitalPinToInterrupt(m2encB), BencoderISR, CHANGE); + attachInterrupt(digitalPinToInterrupt(m3encA), CencoderISR, CHANGE); + attachInterrupt(digitalPinToInterrupt(m3encB), CencoderISR, CHANGE); +} + +void AencoderISR() { + Aencount++; +} +void BencoderISR() { + Bencount++; +} +void CencoderISR() { + Cencount++; +} +void Areadenc() { + ACtime = micros(); + APtime = ACtime - ALtime; + ALtime = ACtime; + Arpm = (Aencount / 211.2) * (60000000.0 / APtime); + Serial.print("Motor A RPM: "); + Serial.print(Arpm); + Serial.print(" Sample period:"); + Serial.print(APtime); + Serial.print("ms, encoder count:"); + Serial.println(Aencount); + Aencount = 0; +} +void Breadenc() { + BCtime = micros(); + BPtime = BCtime - BLtime; + BLtime = BCtime; + Brpm = (Bencount / 211.2) * (60000000.0 / BPtime); + Serial.print("Motor B RPM: "); + Serial.print(Brpm); + Serial.print(" Sample period: "); + Serial.print(BPtime); + Serial.print(" ms, encoder count: "); + Serial.println(Bencount); + Bencount = 0; +} +void Creadenc() { + CCtime = micros(); + CPtime = CCtime - CLtime; + CLtime = CCtime; + Crpm = (Cencount / 211.2) * (60000000.0 / CPtime); + Serial.print("Motor C RPM: "); + Serial.print(Crpm); + Serial.print(" Sample period: "); + Serial.print(CPtime); + Serial.print(" ms, encoder count: "); + Serial.println(Cencount); + Cencount = 0; } -void Amove(int sped){ +void Amove(double sped) { + spdA = abs(sped)*255; digitalWrite(m1enA, HIGH); - digitalWrite(m1enA, LOW); - sp = abs(sped); + digitalWrite(m1enB, LOW); if (sped < 0) { - Serial.print("back"); - analogWrite(m1pwm1, sp); - digitalWrite(m1pwm2, LOW); + Serial.print("Motor A back "); + analogWrite(m1pwm1, spdA); + analogWrite(m1pwm2, 0); } else { - Serial.print("forward"); - digitalWrite(m1pwm1, LOW); - analogWrite(m1pwm2, sp); + Serial.print("Motor A forward "); + analogWrite(m1pwm1, 0); + analogWrite(m1pwm2, spdA); } - Serial.println(sp); + Serial.println(spdA); } -void Bmove(int sped) { - Serial.print("moving B "); +void Bmove(double sped) { + spdB = abs(sped)*255; + digitalWrite(m2enA, HIGH); + digitalWrite(m2enB, LOW); if (sped < 0) { - digitalWrite(in3, LOW); - digitalWrite(in4, HIGH); - Serial.print("back"); + Serial.print("Motor B back "); + analogWrite(m2pwm1, spdB); + analogWrite(m2pwm2, 0); } else { - digitalWrite(in3, HIGH); - digitalWrite(in4, LOW); - Serial.print("forward"); + Serial.print("Motor B forward "); + analogWrite(m2pwm1, 0); + analogWrite(m2pwm2, spdB); } - Serial.print("with speed: "); - int sp = abs(sped); - analogWrite(enB, sp); - Serial.println(sp); + Serial.println(spdB); } -void Cmove(int sped) { - Serial.print("moving C "); +void Cmove(double sped) { + spdC = abs(sped) * 255; + digitalWrite(m3enA, HIGH); + digitalWrite(m3enB, LOW); if (sped < 0) { - digitalWrite(in5, LOW); - digitalWrite(in6, HIGH); - Serial.print("back"); + Serial.print("Motor C back "); + analogWrite(m3pwm1, spdC); + analogWrite(m3pwm2, 0); } else { - digitalWrite(in5, HIGH); - digitalWrite(in6, LOW); - Serial.print("forward"); + Serial.print("Motor C forward "); + analogWrite(m3pwm1, 0); + analogWrite(m3pwm2, spdC); } - Serial.print("with speed: "); - int sp = abs(sped); - analogWrite(enC, sp); - Serial.println(sp); -} - -void turnoff(){ - Serial.println("stop"); - analogWrite(enA, 0); - analogWrite(enB, 0); - analogWrite(enC, 0); - digitalWrite(in1, LOW); - digitalWrite(in2, LOW); - digitalWrite(in3, LOW); - digitalWrite(in4, LOW); - digitalWrite(in5, LOW); - digitalWrite(in6, LOW); -} -void forward(int speed){ - Serial.println("forward"); - analogWrite(enA, speed); - analogWrite(enB, speed); - analogWrite(enC, speed); - digitalWrite(in1, LOW); - digitalWrite(in2, LOW); - digitalWrite(in3, HIGH); - digitalWrite(in4, LOW); - digitalWrite(in5, HIGH); - digitalWrite(in6, LOW); -} -void turn(int speed){ - Serial.println("turn"); - analogWrite(enA, speed); - analogWrite(enB, speed); - analogWrite(enC, speed); - digitalWrite(in1, HIGH); - digitalWrite(in2, LOW); - digitalWrite(in3, HIGH); - digitalWrite(in4, LOW); - digitalWrite(in5, HIGH); - digitalWrite(in6, LOW); + Serial.println(spdC); } void moveohmi(int speed, int direction){ - turnoff(); - double dirrad = (direction*71) / 4068; - dirA = 1.047198-dirrad; - dirB = 3.141593-dirrad; - dirC = 5.235988-dirrad; - spdA = speed*sin(dirA); - spdB = speed*sin(dirB); - spdC = speed*sin(dirC); - Amove(spdA); - Bmove(spdB); - Cmove(spdC); -} -void beddermoveohmi(int speed, int direction){ - turnoff(); + Amove(0); + Bmove(0); + Cmove(0); - double dirrad = (direction*71) / 4068; + double dirrad = (direction*71.0000) / 4068.0000; Serial.println(dirrad); //vector ontb in x en y - double x = sin(dirrad)*speed; - double y = cos(dirrad)*speed; + double y = sin(dirrad); + double x = cos(dirrad); Serial.println((String)"x:"+x+" y:"+y); - spdA = -0.5*x - sqrt(3)/2*y; - spdB = x; - spdC = -0.5*x + sqrt(3)/2*y; - Amove(spdA); - Bmove(spdB); - Cmove(spdC); - - Serial.println(spdA); - Serial.println(spdB); - Serial.println(spdC); + double spdeA = y*speed; + double spdeB = (-0.500*x - sqrt(3.000)/2.000*y)*speed; + double spdeC = (-0.500*x + sqrt(3.000)/2.000*y)*speed; + Serial.println(spdeA); + Amove(spdeA); + Bmove(spdeB); + Cmove(spdeC); Serial.println(); Serial.println(); } -void loop() -{ +void rotate(int rodeg, int speed){ +//use compas heading +} +void demo(){ + + Amove(sp); + Bmove(sp); + Cmove(sp); + Serial.println("seperate A B C rotation"); delay(1000); - turnoff(); - beddermoveohmi(255, 0); + + Amove(0); + Bmove(0); + Cmove(0); + Serial.println("seperate A B C stop"); delay(1000); - turnoff(); - Amove(255); + + Amove(-sp); + Bmove(-sp); + Cmove(-sp); + Serial.println("seperate A B C -rotation"); delay(1000); - turnoff(); - Bmove(255); + + moveohmi(0, 0); + Serial.println("ohmi stop"); delay(1000); - turnoff(); - Cmove(255); + + rotate(90, sp); + Serial.println("rotation function 90deg"); + rotate(90, sp); + Serial.println("rotation function -90deg"); + delay(1000); + + moveohmi(sp, 35); + Serial.println("ohmi move 35deg"); delay(1000); - turnoff(); - turn(254); + + moveohmi(sp, 215); + Serial.println("ohmi move 215deg"); delay(1000); + + for(int i = 0; i<360; i++){ + moveohmi(sp, i); + Serial.println(i); + delay(50); + } + Serial.println("ohmi move circle"); + delay(1000); + +} +void loop(){ + demo(); + delay(100); + } diff --git a/debug/motordriver/onemotor/onemotor.ino b/debug/motordriver/onemotor/onemotor.ino new file mode 100644 index 0000000..f3d91e6 --- /dev/null +++ b/debug/motordriver/onemotor/onemotor.ino @@ -0,0 +1,88 @@ +#include + +int enA = 1; +int enB = 2; +int pwm1 = 3; +int pwm2 = 4; +int encoA = 5; +int encoB = 6; + +int speed = 100; // speed 0-100 + +double sp = 0.00; +double rpm = 0.00; +volatile long encount = 0; +unsigned long Ltime = 0; +unsigned long Ctime = 0; +unsigned long Ptime = 0; + +void setup() { + pinMode(enA, OUTPUT); + pinMode(enB, OUTPUT); + pinMode(pwm1, OUTPUT); + pinMode(pwm2, OUTPUT); + + pinMode(encoA, INPUT_PULLUP); + pinMode(encoB, INPUT_PULLUP); + + attachInterrupt(digitalPinToInterrupt(encoA), encoderISR, CHANGE); + attachInterrupt(digitalPinToInterrupt(encoB), encoderISR, CHANGE); + + Serial.begin(9600); +} + +void encoderISR() { + encount++; +} + +void readenc() { + Ctime = micros(); + Ptime = Ctime - Ltime; + Ltime = Ctime; + rpm = (encount / 211.2) * (60000000.0 / Ptime); + Serial.print("RPM: "); + Serial.print(rpm); + Serial.print(" Sample period:"); + Serial.print(Ptime); + Serial.print("ms, encoder count:"); + Serial.println(encount); + + encount = 0; +} +void resetenc(){ + Ctime = micros(); + Ltime = Ctime; + encount = 0; +} + +void move(int sped) { + sp = abs(sped)*2.55; + digitalWrite(enA, HIGH); + digitalWrite(enB, LOW); + if (sped < 0) { + Serial.print("back "); + analogWrite(pwm1, sp); + analogWrite(pwm2, 0); + } else { + Serial.print("forward "); + analogWrite(pwm1, 0); + analogWrite(pwm2, sp); + } + Serial.println(sp); +} + +void loop() { + move(speed); + delay(1000); + readenc(); + + + move(0); + resetenc(); + delay(1000); + readenc(); + + move(-speed); + delay(1000); + readenc(); +} diff --git a/poster.svg b/poster.svg index 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e=this.a*t.a+this.c*t.b,s=this.b*t.a+this.d*t.b,r=this.a*t.c+this.c*t.d,n=this.b*t.c+this.d*t.d,o=this.a*t.e+this.c*t.f+this.e,i=this.b*t.e+this.d*t.f+this.f;return new g(e,s,r,n,o,i)}}class w{constructor(t,e){this.nodes=t,this.colors=e}paintCurve(t,e){if(o(this.nodes)>r){const s=n(...this.nodes);let r=[[],[]],o=[[],[]];for(let t=0;t<4;++t)r[0][t]=this.colors[0][t],r[1][t]=(this.colors[0][t]+this.colors[1][t])/2,o[0][t]=r[1][t],o[1][t]=this.colors[1][t];let i=new w(s[0],r),a=new w(s[1],o);i.paintCurve(t,e),a.paintCurve(t,e)}else{let s=Math.round(this.nodes[0].x);if(s>=0&&s<e){let r=4*(~~this.nodes[0].y*e+s);t[r]=Math.round(this.colors[0][0]),t[r+1]=Math.round(this.colors[0][1]),t[r+2]=Math.round(this.colors[0][2]),t[r+3]=Math.round(this.colors[0][3])}}}}class m{constructor(t,e){this.nodes=t,this.colors=e}split(){let t=[[],[],[],[]],e=[[],[],[],[]],s=[[[],[]],[[],[]]],r=[[[],[]],[[],[]]];for(let s=0;s<4;++s){const r=n(this.nodes[0][s],this.nodes[1][s],this.nodes[2][s],this.nodes[3][s]);t[0][s]=r[0][0],t[1][s]=r[0][1],t[2][s]=r[0][2],t[3][s]=r[0][3],e[0][s]=r[1][0],e[1][s]=r[1][1],e[2][s]=r[1][2],e[3][s]=r[1][3]}for(let t=0;t<4;++t)s[0][0][t]=this.colors[0][0][t],s[0][1][t]=this.colors[0][1][t],s[1][0][t]=(this.colors[0][0][t]+this.colors[1][0][t])/2,s[1][1][t]=(this.colors[0][1][t]+this.colors[1][1][t])/2,r[0][0][t]=s[1][0][t],r[0][1][t]=s[1][1][t],r[1][0][t]=this.colors[1][0][t],r[1][1][t]=this.colors[1][1][t];return[new m(t,s),new m(e,r)]}paint(t,e){let s,n=!1;for(let t=0;t<4;++t)if((s=o([this.nodes[0][t],this.nodes[1][t],this.nodes[2][t],this.nodes[3][t]]))>r){n=!0;break}if(n){let s=this.split();s[0].paint(t,e),s[1].paint(t,e)}else{new w([...this.nodes[0]],[...this.colors[0]]).paintCurve(t,e)}}}class b{constructor(t){this.readMesh(t),this.type=t.getAttribute("type")||"bilinear"}readMesh(t){let e=[[]],s=[[]],r=Number(t.getAttribute("x")),n=Number(t.getAttribute("y"));e[0][0]=new x(r,n);let o=t.children;for(let t=0,r=o.length;t<r;++t){e[3*t+1]=[],e[3*t+2]=[],e[3*t+3]=[],s[t+1]=[];let r=o[t].children;for(let n=0,o=r.length;n<o;++n){let o=r[n].children;for(let r=0,i=o.length;r<i;++r){let i=r;0!==t&&++i;let h,d=o[r].getAttribute("path"),c="l";null!=d&&(c=(h=d.match(/\s*([lLcC])\s*(.*)/))[1]);let u=l(h[2]);switch(c){case"l":0===i?(e[3*t][3*n+3]=u[0].add(e[3*t][3*n]),e[3*t][3*n+1]=a(e[3*t][3*n],e[3*t][3*n+3]),e[3*t][3*n+2]=a(e[3*t][3*n+3],e[3*t][3*n])):1===i?(e[3*t+3][3*n+3]=u[0].add(e[3*t][3*n+3]),e[3*t+1][3*n+3]=a(e[3*t][3*n+3],e[3*t+3][3*n+3]),e[3*t+2][3*n+3]=a(e[3*t+3][3*n+3],e[3*t][3*n+3])):2===i?(0===n&&(e[3*t+3][3*n+0]=u[0].add(e[3*t+3][3*n+3])),e[3*t+3][3*n+1]=a(e[3*t+3][3*n],e[3*t+3][3*n+3]),e[3*t+3][3*n+2]=a(e[3*t+3][3*n+3],e[3*t+3][3*n])):(e[3*t+1][3*n]=a(e[3*t][3*n],e[3*t+3][3*n]),e[3*t+2][3*n]=a(e[3*t+3][3*n],e[3*t][3*n]));break;case"L":0===i?(e[3*t][3*n+3]=u[0],e[3*t][3*n+1]=a(e[3*t][3*n],e[3*t][3*n+3]),e[3*t][3*n+2]=a(e[3*t][3*n+3],e[3*t][3*n])):1===i?(e[3*t+3][3*n+3]=u[0],e[3*t+1][3*n+3]=a(e[3*t][3*n+3],e[3*t+3][3*n+3]),e[3*t+2][3*n+3]=a(e[3*t+3][3*n+3],e[3*t][3*n+3])):2===i?(0===n&&(e[3*t+3][3*n+0]=u[0]),e[3*t+3][3*n+1]=a(e[3*t+3][3*n],e[3*t+3][3*n+3]),e[3*t+3][3*n+2]=a(e[3*t+3][3*n+3],e[3*t+3][3*n])):(e[3*t+1][3*n]=a(e[3*t][3*n],e[3*t+3][3*n]),e[3*t+2][3*n]=a(e[3*t+3][3*n],e[3*t][3*n]));break;case"c":0===i?(e[3*t][3*n+1]=u[0].add(e[3*t][3*n]),e[3*t][3*n+2]=u[1].add(e[3*t][3*n]),e[3*t][3*n+3]=u[2].add(e[3*t][3*n])):1===i?(e[3*t+1][3*n+3]=u[0].add(e[3*t][3*n+3]),e[3*t+2][3*n+3]=u[1].add(e[3*t][3*n+3]),e[3*t+3][3*n+3]=u[2].add(e[3*t][3*n+3])):2===i?(e[3*t+3][3*n+2]=u[0].add(e[3*t+3][3*n+3]),e[3*t+3][3*n+1]=u[1].add(e[3*t+3][3*n+3]),0===n&&(e[3*t+3][3*n+0]=u[2].add(e[3*t+3][3*n+3]))):(e[3*t+2][3*n]=u[0].add(e[3*t+3][3*n]),e[3*t+1][3*n]=u[1].add(e[3*t+3][3*n]));break;case"C":0===i?(e[3*t][3*n+1]=u[0],e[3*t][3*n+2]=u[1],e[3*t][3*n+3]=u[2]):1===i?(e[3*t+1][3*n+3]=u[0],e[3*t+2][3*n+3]=u[1],e[3*t+3][3*n+3]=u[2]):2===i?(e[3*t+3][3*n+2]=u[0],e[3*t+3][3*n+1]=u[1],0===n&&(e[3*t+3][3*n+0]=u[2])):(e[3*t+2][3*n]=u[0],e[3*t+1][3*n]=u[1]);break;default:console.error("mesh.js: "+c+" invalid path type.")}if(0===t&&0===n||r>0){let e=window.getComputedStyle(o[r]).stopColor.match(/^rgb\s*\(\s*(\d+)\s*,\s*(\d+)\s*,\s*(\d+)\s*\)$/i),a=window.getComputedStyle(o[r]).stopOpacity,h=255;a&&(h=Math.floor(255*a)),e&&(0===i?(s[t][n]=[],s[t][n][0]=Math.floor(e[1]),s[t][n][1]=Math.floor(e[2]),s[t][n][2]=Math.floor(e[3]),s[t][n][3]=h):1===i?(s[t][n+1]=[],s[t][n+1][0]=Math.floor(e[1]),s[t][n+1][1]=Math.floor(e[2]),s[t][n+1][2]=Math.floor(e[3]),s[t][n+1][3]=h):2===i?(s[t+1][n+1]=[],s[t+1][n+1][0]=Math.floor(e[1]),s[t+1][n+1][1]=Math.floor(e[2]),s[t+1][n+1][2]=Math.floor(e[3]),s[t+1][n+1][3]=h):3===i&&(s[t+1][n]=[],s[t+1][n][0]=Math.floor(e[1]),s[t+1][n][1]=Math.floor(e[2]),s[t+1][n][2]=Math.floor(e[3]),s[t+1][n][3]=h))}}e[3*t+1][3*n+1]=new x,e[3*t+1][3*n+2]=new x,e[3*t+2][3*n+1]=new x,e[3*t+2][3*n+2]=new x,e[3*t+1][3*n+1].x=(-4*e[3*t][3*n].x+6*(e[3*t][3*n+1].x+e[3*t+1][3*n].x)+-2*(e[3*t][3*n+3].x+e[3*t+3][3*n].x)+3*(e[3*t+3][3*n+1].x+e[3*t+1][3*n+3].x)+-1*e[3*t+3][3*n+3].x)/9,e[3*t+1][3*n+2].x=(-4*e[3*t][3*n+3].x+6*(e[3*t][3*n+2].x+e[3*t+1][3*n+3].x)+-2*(e[3*t][3*n].x+e[3*t+3][3*n+3].x)+3*(e[3*t+3][3*n+2].x+e[3*t+1][3*n].x)+-1*e[3*t+3][3*n].x)/9,e[3*t+2][3*n+1].x=(-4*e[3*t+3][3*n].x+6*(e[3*t+3][3*n+1].x+e[3*t+2][3*n].x)+-2*(e[3*t+3][3*n+3].x+e[3*t][3*n].x)+3*(e[3*t][3*n+1].x+e[3*t+2][3*n+3].x)+-1*e[3*t][3*n+3].x)/9,e[3*t+2][3*n+2].x=(-4*e[3*t+3][3*n+3].x+6*(e[3*t+3][3*n+2].x+e[3*t+2][3*n+3].x)+-2*(e[3*t+3][3*n].x+e[3*t][3*n+3].x)+3*(e[3*t][3*n+2].x+e[3*t+2][3*n].x)+-1*e[3*t][3*n].x)/9,e[3*t+1][3*n+1].y=(-4*e[3*t][3*n].y+6*(e[3*t][3*n+1].y+e[3*t+1][3*n].y)+-2*(e[3*t][3*n+3].y+e[3*t+3][3*n].y)+3*(e[3*t+3][3*n+1].y+e[3*t+1][3*n+3].y)+-1*e[3*t+3][3*n+3].y)/9,e[3*t+1][3*n+2].y=(-4*e[3*t][3*n+3].y+6*(e[3*t][3*n+2].y+e[3*t+1][3*n+3].y)+-2*(e[3*t][3*n].y+e[3*t+3][3*n+3].y)+3*(e[3*t+3][3*n+2].y+e[3*t+1][3*n].y)+-1*e[3*t+3][3*n].y)/9,e[3*t+2][3*n+1].y=(-4*e[3*t+3][3*n].y+6*(e[3*t+3][3*n+1].y+e[3*t+2][3*n].y)+-2*(e[3*t+3][3*n+3].y+e[3*t][3*n].y)+3*(e[3*t][3*n+1].y+e[3*t+2][3*n+3].y)+-1*e[3*t][3*n+3].y)/9,e[3*t+2][3*n+2].y=(-4*e[3*t+3][3*n+3].y+6*(e[3*t+3][3*n+2].y+e[3*t+2][3*n+3].y)+-2*(e[3*t+3][3*n].y+e[3*t][3*n+3].y)+3*(e[3*t][3*n+2].y+e[3*t+2][3*n].y)+-1*e[3*t][3*n].y)/9}}this.nodes=e,this.colors=s}paintMesh(t,e){let 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